Search

We present an algorithm to find first order saddle points on the potential energy surface (PES). The algorithm is formulated as a constrained optimization problem that involves two sets of atomic coordinates (images), a time-varying distance constraint and a constraint on the energy difference. Both images start in different valleys of the PES and are pulled toward each other by gradually reducing the distance. The search space is restricted to the pairs of configurations that share the same potential energy. By minimizing the energy while the distance shrinks, a minimum of the constrained search space is tracked. In simple cases, the two images are confined to their respective sides of the barrier until they finally converge near the saddle point. If one image accidentally crosses the barrier, the path is split at suitable locations and the algorithm is repeated recursively. The optimization is implemented as a combination of a quasi-Newton optimization and a linear constraint. The method was tested on a set of Lennard-Jones-38 cluster transitions and a set of 121 molecular reactions using density functional theory calculations. The efficiency in terms of energy and force evaluation is better than with competing methods as long as they do not switch to single-ended methods. The construction of a continuous search path with small steps and the ability to focus on arbitrary subsegments of the path provide an additional value in terms of robustness and flexibility. [ABSTRACT FROM AUTHOR]

Derivative-free optimization (DFO) consists in finding the best value of an objective function without relying on derivatives. To tackle such problems, one may build approximate derivatives, using for instance finite-difference estimates. One may also design algorithmic strategies that perform space exploration and seek improvement over the current point. The first type of strategy often provides good performance on smooth problems but at the expense of more function evaluations. The second type is cheaper and typically handles non-smoothness or noise in the objective better. Recently, full-low evaluation methods have been proposed as a hybrid class of DFO algorithms that combine both strategies, respectively denoted as Full-Eval and Low-Eval. In the unconstrained case, these methods showed promising numerical performance. In this paper, we extend the full-low evaluation framework to bound and linearly constrained derivative-free optimization. We derive convergence results for an instance of this framework, that combines finite-difference quasi-Newton steps with probabilistic direct-search steps. The former are projected onto the feasible set, while the latter are defined within tangent cones identified by nearby active constraints. We illustrate the practical performance of our instance on standard linearly constrained problems, that we adapt to introduce noisy evaluations as well as non-smoothness. In all cases, our method performs favorably compared to algorithms that rely solely on Full-eval or Low-eval iterations. [ABSTRACT FROM AUTHOR]

Recently, the proximal Newton-type method and its variants have been generalized to solve composite optimization problems over the Stiefel manifold whose objective function is the summation of a smooth function and a nonsmooth function. In this paper, we propose an adaptive quadratically regularized proximal quasi-Newton method, named ARPQN, to solve this class of problems. Under some mild assumptions, the global convergence, the local linear convergence rate and the iteration complexity of ARPQN are established. Numerical experiments and comparisons with other state-of-the-art methods indicate that ARPQN is very promising. We also propose an adaptive quadratically regularized proximal Newton method, named ARPN. It is shown the ARPN method has a local superlinear convergence rate under certain reasonable assumptions, which demonstrates attractive convergence properties of regularized proximal Newton methods. [ABSTRACT FROM AUTHOR]

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In practical application, existing two-point magnetic gradient tensor (MGT) localization methods have a maximum detection distance of only 2.5 m, and the magnetic moment vectors of measured targets are all unknown. In order to realize remote, real-time localization, a new two-point magnetic localization method based on self-developed, ultra-sensitive superconducting quantum interference device (SQUID) magnetometers and MGT invariants is proposed. Both the magnetic moment vector and the relative position vector can be directly calculated based on the linear positioning model, and a quasi-Newton optimization algorithm is adopted to further improve the interference suppression capability. The simulation results show that the detection distance of the proposed method can reach 500 m when the superconducting MGT measurement system is used. Compared with Nara's single-point tensor (NSPT) method and Xu's two-point tensor (XTPT) method, the proposed method produces the smallest relative localization error (i.e., significantly less than 1% in the non-positioning blind area) without sacrificing real-time characteristics. The causes of and solutions to the positioning blind area are also analyzed. The equivalent experiments, which were conducted with a detection distance of 10 m, validate the effectiveness of the localization method, yielding a minimum relative localization error of 4.5229%. [ABSTRACT FROM AUTHOR]

Dipole localization, a fundamental challenge in electromagnetic source imaging, inherently constitutes an optimization problem aimed at solving the inverse problem of electric current source estimation within the human brain. The accuracy of dipole localization algorithms is contingent upon the complexity of the forward model, often referred to as the head model, and the signal-to-noise ratio (SNR) of measurements. In scenarios characterized by low SNR, often corresponding to deep-seated sources, existing optimization techniques struggle to converge to global minima, thereby leading to the localization of dipoles at erroneous positions, far from their true locations. This study presents a novel hybrid algorithm that combines simulated annealing with the traditional quasi-Newton optimization method, tailored to address the inherent limitations of dipole localization under low-SNR conditions. Using a realistic head model for both electroencephalography (EEG) and magnetoencephalography (MEG), it is demonstrated that this novel hybrid algorithm enables significant improvements of up to 45% in dipole localization accuracy compared to the often-used dipole scanning and gradient descent techniques. Localization improvements are not only found for single dipoles but also in two-dipole-source scenarios, where sources are proximal to each other. The novel methodology presented in this work could be useful in various applications of clinical neuroimaging, particularly in cases where recordings are noisy or sources are located deep within the brain. [ABSTRACT FROM AUTHOR]

In this paper, we study the stationary Black-Scholes model arising in finance with transaction costs. This model becomes interesting when the time does not play a role such as, for instance, in perpetual options. The equation describing this model is a nonlinear second-order boundary value problem and there is no analytic solutions in closed form for such a nonlinear equation. After discretization via the centered finite difference formula we have to solve a nonlinear algebraic system which would be a serious problem when we use a small discretization mesh. We solve this nonlinear system by the residual-based Broyden's method, which is an efficient quasi-Newton method and is convenient to implement by a desk computer. We give a convergence analysis of the Broyden's method by assuming a lower and upper bound of the converged solution of the Black-Scholes model. Numerical results are given to show that the convergence rate of the method is robust with respect to the discretization mesh and the problem parameters. [ABSTRACT FROM AUTHOR]

In this work, we introduce a novel stochastic second-order method, within the framework of a non-monotone trust-region approach, for solving the unconstrained, nonlinear, and non-convex optimization problems arising in the training of deep neural networks. The proposed algorithm makes use of subsampling strategies that yield noisy approximations of the finite sum objective function and its gradient. We introduce an adaptive sample size strategy based on inexpensive additional sampling to control the resulting approximation error. Depending on the estimated progress of the algorithm, this can yield sample size scenarios ranging from mini-batch to full sample functions. We provide convergence analysis for all possible scenarios and show that the proposed method achieves almost sure convergence under standard assumptions for the trust-region framework. We report numerical experiments showing that the proposed algorithm outperforms its state-of-the-art counterpart in deep neural network training for image classification and regression tasks while requiring a significantly smaller number of gradient evaluations. [ABSTRACT FROM AUTHOR]

Is it possible for a first-order method, i.e., only first derivatives allowed, to be quadratically convergent? For univariate loss functions, the answer is yes—the Steffensen method avoids second derivatives and is still quadratically convergent like Newton method. By incorporating a specific step size we can even push its convergence order beyond quadratic to 1 + 2 ≈ 2.414 . While such high convergence orders are a pointless overkill for a deterministic algorithm, they become rewarding when the algorithm is randomized for problems of massive sizes, as randomization invariably compromises convergence speed. We will introduce two adaptive learning rates inspired by the Steffensen method, intended for use in a stochastic optimization setting and requires no hyperparameter tuning aside from batch size. Extensive experiments show that they compare favorably with several existing first-order methods. When restricted to a quadratic objective, our stochastic Steffensen methods reduce to randomized Kaczmarz method—note that this is not true for SGD or SLBFGS—and thus we may also view our methods as a generalization of randomized Kaczmarz to arbitrary objectives. [ABSTRACT FROM AUTHOR]

In this paper, an augmented memoryless BFGS quasi-Newton method was proposed for solving unconstrained optimization problems. Based on a new modified secant equation, an augmented memoryless BFGS update formula and an efficient optimization algorithm were established. To improve the stability of the numerical experiment, we obtained the scaling parameter by minimizing the upper bound of the condition number. The global convergence of the algorithm was proved, and numerical experiments showed that the algorithm was efficient. [ABSTRACT FROM AUTHOR]

Introduction. Methods of unconstrained optimization play a significant role in machine learning [1–6]. When solving practical problems in machine learning, such as tuning nonlinear regression models, the extremum point of the chosen optimality criterion is often degenerate, which significantly complicates its search. Therefore, degenerate problems are the most challenging in optimization. Known numerical methods for solving the general unconstrained optimization problem, up to the second order, have very low convergence rates when solving degenerate problems [7, 8]. This is explained by the fact that for a significant improvement in convergence rate in this case, it is necessary to use higher-order derivatives in the method than the second order [10]. The purpose of the paper is to develop an efficient quasi-Newton method for solving degenerate unconstrained optimization problems, the idea of which (unlike regularization) involves dividing the entire space into the sum of two orthogonal subspaces. This idea was introduced in [23]. The space division at each iteration of the method is based on the spectral decomposition of the matrix approximating the Hessian of the objective function using the BFGS formula [3]. Each subspace exhibits its own behavior of the objective function, and therefore, an appropriate minimization method is applied on it. Results. A combined quasi-Newton method is presented for solving degenerate unconstrained optimization problems, based on orthogonal decomposition of the Hessian approximation matrix and division of the entire space into the sum of two orthogonal subspaces. On one subspace (the kernel of the Hessian approximation matrix), a method is applied where derivatives in the direction of the 4th order are computed, while on the orthogonal complement to it, a quasi-Newtonian method is applied. A separate one-dimensional search is applied on each of these subspaces to determine the step multiplier in the respective direction. The effectiveness of the presented combined method is confirmed by numerical experiments conducted on widely accepted test functions for unconstrained optimization problems. The proposed method allows obtaining fairly accurate solutions to test tasks in case of degeneracy of the minimum point with significantly lower computational costs for gradient calculations compared to optimization procedures of well-known mathematical packages. Conclusions. The idea of dividing the entire space into the sum of two (or possibly more) orthogonal subspaces when solving complex optimization problems is quite promising in terms of applying a combination of different numerical methods on separate subspaces. In the future, it is planned to conduct theoretical research on the convergence rate of the presented combined method in solving degenerate unconstrained optimization problems.

This paper presents modified memoryless quasi-Newton methods based on the spectral-scaling Broyden family on Riemannian manifolds. The method involves adding one parameter to the search direction of the memoryless self-scaling Broyden family on the manifold. Moreover, it uses a general map instead of vector transport. This idea has already been proposed within a general framework of Riemannian conjugate gradient methods where one can use vector transport, scaled vector transport, or an inverse retraction. We show that the search direction satisfies the sufficient descent condition under some assumptions on the parameters. In addition, we show global convergence of the proposed method under the Wolfe conditions. We numerically compare it with existing methods, including Riemannian conjugate gradient methods and the memoryless spectral-scaling Broyden family. The numerical results indicate that the proposed method with the BFGS formula is suitable for solving an off-diagonal cost function minimization problem on an oblique manifold. [ABSTRACT FROM AUTHOR]

A phase field modeling framework for fatigue fracture was proposed in functionally graded materials (FGMs). This framework is constructed based on homogenization theory and takes into consideration the spatial variation of effective properties, critical energy release rate, and fatigue degradation function. Several exemplary cases are shown according to the model to prove the capabilities of the presented framework. These cases present fatigue crack propagation and crack length variation, and the influences of cyclic load, the nonhomogeneous and geometric parameters on crack propagation and crack length. The framework enables capture fatigue crack propagation in FGMs under cyclic loading and considering the spatial variation of effective properties, critical energy release rate, and fatigue degradation function. Furthermore, a monolithic scheme applying the quasi-Newton method to address the issue of fatigue fracture in FGMs is proposes. [ABSTRACT FROM AUTHOR]

We present a new diagonal quasi-Newton method for solving unconstrained optimization problems based on the weak secant equation. To control the diagonal elements, the new method uses new criteria to generate the Hessian approximation. We establish the global convergence of the proposed method with the Armijo line search. Numerical results on a collection of standard test problems demonstrate the superiority of the proposed method over several existing diagonal methods. [ABSTRACT FROM AUTHOR]

In this work, we study the convergence and performance of nonlinear solvers for the Bidomain equations after decoupling the ordinary and partial differential equations of the cardiac system. Firstly, we provide a rigorous proof of the global convergence of Quasi-Newton methods, such as BFGS, and nonlinear Conjugate-Gradient methods, such as Fletcher–Reeves, for the Bidomain system, by analyzing an auxiliary variational problem under physically reasonable hypotheses. Secondly, we compare several nonlinear Bidomain solvers in terms of execution time, robustness with respect to the data and parallel scalability. Our findings indicate that Quasi-Newton methods are the best choice for nonlinear Bidomain systems, since they exhibit faster convergence rates compared to standard Newton-Krylov methods, while maintaining robustness and scalability. Furthermore, first-order methods also demonstrate competitiveness and serve as a viable alternative, particularly for matrix-free implementations that are well-suited for GPU computing. [ABSTRACT FROM AUTHOR]

The cloud storage service, known for its flexible and expandable nature, often has difficulties managing operating costs while ensuring dependable service and quick response times. This investigation presents a novel approach to optimizing cost efficiency in cloud storage systems by applying particle swarm optimization of the Markovian retrial queueing model in a generic setup by incorporating the working vacation and users' discouragement behavior. Some users may opt not to enter the system or join the retry pool to wait for their turn if the server is occupied. After returning from working vacation, if there is one user available for service, the server can interrupt the vacation period. The server is subject to breakdown and can be recovered after getting the repair. In the proposed model, the server is prone to catastrophes and can fail at any time, leading to the entire system breaking down, and no users being able to access it during this period. Chapman–Kolmogorov (CK) steady-state equations associated with the quasi-birth-death (QBD) process are constructed to make a mathematical design. The governing equations framed to derive the queue length distributions and various performance indices are solved using the recursive method and difference equation theory. The fuzzified parameters are used to develop the FM/FM/1/WV model, which is analyzed using a parametric nonlinear programming approach. To determine the optimal design parameters, the cost minimization problem has been done using the quasi-Newton method and particle swarm optimization. This model incorporates features such as server failures, retrials, and catastrophes, thereby reflecting the complex nature of cloud storage operations. A suitable illustration of cloud storage is taken for both classical and fuzzified models to facilitate the numerical results of performance indices and optimal decision descriptors. [ABSTRACT FROM AUTHOR]

When applied to linear vector sequences, extrapolation methods are equivalent to Krylov subspace methods. Both types of methods can be expressed as particular cases of the multisecant equations, the secant method generalized to higher dimensions. Through these equations, there is also equivalence with a variety of quasi-Newton methods. This paper presents a framework to connect these various methods. [ABSTRACT FROM AUTHOR]

ABSRACTThis study introduces a novel theory employing four unknowns to examine bending of a double-curvature functionally graded shells experiencing both uniform and sinusoidal pressure. This investigation utilizes 2D and quasi-3D higher order shear deformation theories, integrating a fresh model of a high-order displacement field. It focuses on exploring how geometric ratios, volume fraction and power law index influence the bending behavior, specifically examining their effects on the normal and shear stresses variation, along with their amplification-reduction impacts. The effectiveness of the developed model is evaluated by comparing its performance in simulating bending characteristics of plates, cylinders, spheres and ellipses with those presented in literature. [ABSTRACT FROM AUTHOR]

In this paper, a new appropriate diagonal matrix estimation of the Hessian is introduced by minimizing the Byrd and Nocedal function subject to the weak secant equation. The Hessian estimate is used to correct the framework of a nonmonotone trust region algorithm with the regularized quasi-Newton method. Moreover, to counteract the adverse effect of monotonicity, we introduce a new nonmonotone strategy. The global and superlinear convergence of the suggested algorithm is established under some standard conditions. The numerical experiments on unconstrained optimization test functions show that the new algorithm is efficient and robust. [ABSTRACT FROM AUTHOR]

It is usually not possible to solve partial differential equations, especially the delay type, with analytical methods. Therefore, in this article, we present an efficient method for solving differential equations of the difference delayed reaction-diffusion type, which can be generalized to other delayed partial differential equations. In the proposed approach, we first convert the delayed equation into an equivalent non-delayed equation by inserting the corresponding delay function with an effective technique. Then, using a pseudo-spectral method, we discretize the obtained equation in the Legendre-Gauss-Lobatto collocation points and present an algebraic system with an equal number of equations and unknowns which can be solved by quasi-Newton methods such as Levenderg-Marquardt algorithm. The approximate solutions can be obtained with exponential accuracy. The convergence analysis of the method is fully discussed and four examples are presented to evaluate the results and compare with one of the conventional methods used to solve partial differential equations, that is, the compact finite difference method. [ABSTRACT FROM AUTHOR]

The numerical approximation of the solution to Hamilton-Jacobi-Bellman (HJB) partial differential equations (PDEs) in constrained optimal control problems (COCPs) with nonquadratic functional is studied in this investigation. Discretizing both of the space and time of HJB PDE by the Legendre collocation method, a nonlinear system of algebraic equations is obtained to find the expansion coefficients of the approximate solution. However, solving the system of nonlinear algebraic equations is generally relatively difficult and time-consuming. To improve the implementation of the method, we combine the Legendre collocation method with the policy iteration (PI) algorithm. This process leads to a sequence of linear systems of algebraic equations to find the expansion coefficients. The convergence results for the proposed method are provided. Moreover, it is shown that the PI algorithm for a class of constrained optimal control problems with odd nonquadratic functionals is mathematically equivalent to the quasi-Newton's iteration. Finally, the efficiency and accuracy of the method are demonstrated by solving a number of examples. [ABSTRACT FROM AUTHOR]

The present work aims to investigate the dynamic behavior of a bidirectional functionally graded (BDFG) beam lying on nonlinear elastic substrate tacking into account the impact of the material distribution. For the first time, this effect will be studied. The beam characteristics are considered to change in the axial and thickness directions as a function of a specific function with four distinct distribution models. The BDFG beam is supposed to be in contact with a nonlinear three-parameter substrate with general boundary conditions. Hamilton's principle is used to determine the governing equations based on a quasi-3D solution. An analytical solution is then is applied to obtain the free and forced vibration parameters of the BDFG beam. Furthermore, the validation results show excellent agreement between the proposed theory and those given in the literature. On the other hand, a set of numerical results is exposed and discussed to assess the influence of several geometric and mechanical parameters like distribution patterns of material, beam geometry, foundation's parameters and external force on the forced and the free vibration of a BDFG beam sustained by a nonlinear elastic foundation. The results show that these parameters have a major influence on the dynamic response of BDFG beams supported by nonlinear foundation. These results can be used as reference solutions for future investigations. [ABSTRACT FROM AUTHOR]

We propose a portfolio optimization method with a multi-trend objective and an accelerated quasi-Newton method (MTO-AQNM). It leverages a BFGS-based quasi-Newton algorithm and incorporates an ℓ 1 regularization term and the self-funding constraint. The MTO is designed to identify multiple trend reversals. Different trend reversals are asymmetric, and we hoped to extract rich and effective information from them. The AQNM adopts the BFGS method with the Wolfe conditions, which reduces computational complexity and improves convergence speed. We wanted to evaluate the performance of our algorithm through financial markets that were asymmetric in all respects. To this end, we conducted comprehensive experimental approaches on six benchmark data sets of real-world financial markets that were asymmetric in time, frequency, and asset type. Our method demonstrated superior performance over other state-of-the-art competitors across several mainstream evaluation metrics. [ABSTRACT FROM AUTHOR]

In this paper, a novel non-convex fractional-order image denoising model is proposed to suppress the staircase effect produced by the TV model while maintaining a neat contour. The model combines ℓ q (0 < q < 1) quasi-norm and fractional-order regularization, and employs a diffusion coefficient with a faster convergence rate to preserve more image edges and details. Additionally, an adaptive regularization parameter is designed to adjust the denoising performance of the algorithm. To obtain the optimal approximate solution of the model, an enhanced primal-dual algorithm is adopted and the complexity and convergence of the algorithm are theoretically analyzed. Finally, the effectiveness of the proposed method is demonstrated through numerical experiments. • A new non-convex FOTV model is proposed. • A new diffusion coefficient is introduced to retain more edge details of the image. • The existing primal-dual algorithm is improved, and the convergence of this algorithm is analyzed. • An adaptive regularization parameter is designed. [ABSTRACT FROM AUTHOR]

Recently, structured nonlinear least-squares (NLS) based algorithms gained considerable emphasis from researchers; this attention may result from increasingly applicable areas of these algorithms in different science and engineering domains. In this article, we coined a new efficient structured-based NLS algorithm. We developed a diagonal Hessian-based formulation for solving NLS problems. We derived the quasi-Newton update based on a diagonal matrix scheme subject to a modified structured secant condition. Also, we show that the algorithm's search direction satisfies a sufficient descent condition under some standard assumptions. Subsequently, we also prove the global convergence of the algorithm and then eventually show its linear convergence rate for strongly convex functions. Furthermore, to show case the proposed algorithm's performance, we experimented numerically by comparing it with other approaches on some benchmark test functions available in the literature. Finally, the introduced scheme is applied to solve some data-fitting problems [ABSTRACT FROM AUTHOR]

We propose a modified BFGS algorithm for multiobjective optimization problems with global convergence, even in the absence of convexity assumptions on the objective functions. Furthermore, we establish a local superlinear rate of convergence of the method under usual conditions. Our approach employs Wolfe step sizes and ensures that the Hessian approximations are updated and corrected at each iteration to address the lack of convexity assumption. Numerical results shows that the introduced modifications preserve the practical efficiency of the BFGS method. [ABSTRACT FROM AUTHOR]

The cubature Kalman filter (CKF) based on maximum correntropy criterion (MCC) is robust under non‐Gaussian noises, but it may encounter numerical problems when there are large outliers. First, based on the MCC and weighted least square (WLS) methods, a new cost function is introduced to calculate the state and covariance updates, which can better solve numerical problems caused by large outliers. Then, a nonlinear measurement function is used, and the measurement information is updated through the latest iterative values, which can obtain more accurate results under various non‐Gaussian noises. In addition, the Gauss–Newton, Levenberg–Marquardt, and Quasi–Newton methods are used, and three iterative algorithms named GN‐IMCC‐CKF, LM‐IMCC‐CKF, and QN‐IMCC‐CKF are respectively derived for the updating steps. Compared with the existing algorithms, the simulation results of two classical models show that the proposed algorithms have better numerical stability and estimation accuracy under non‐Gaussian systems. [ABSTRACT FROM AUTHOR]

The need for reconstruction of the distribution of physical properties like dielectric permittivity and electrical conductivity of shallow subsurface sedimentary architecture leads to the development of an optimum strategy of GPR data inversion. In this paper, we present finite difference frequency domain (FDFD) full waveform inversion (FWI) method to get high-resolution subsurface model using GPR data. FWI is an optimization technique which involves in search of the minima between recorded and predicted data. The inversion process includes the quasi-Newton method and simultaneous frequency sampling strategy of irregular sampling. The Hessian term in quasi-Newton algorithm is approximated using preconditioned-LBFGS consideration and the search directions are also optimized after following the Wolfe conditions. At the end of each iteration during inversion, permittivity and conductivity models were updated and became ready to be the initial model for the next iteration. The goals of this research were to develop a robust framework for sedimentary-GPR data inversion and to evaluate the efficacy of the novel grid strategy introduced by Layek and Sengupta (2021) proposed for FWI. This paper presents a comparative analysis between conventional and newly proposed technique from Layek and Sengupta (2021), supported by numerical experiments conducted through our own MATLAB programming. Numerical tests conducted on a benchmark from previously published article, established the fact that new grid formulation produces a faster converging rate and required less computation time. This approach demonstrates remarkable efficacy when applied to a comprehensive sedimentary model comprising a lossy medium. [ABSTRACT FROM AUTHOR]

Chiral metasurface based on bound state in the continuum (BIC) possesses extremely high Q factor. However, intrinsic chiral BIC only can be realized by breaking out‐of‐plane mirror symmetry with complicated 3D structures. In this work, a design of planar intrinsic chiral metasurface supporting orthogonal BICs is proposed. The coupling strength, eigenfrequency, and radiation loss of the two quasi‐BICs can be tuned by metasurface parameters. By adjusting the metasurface parameters, the two quasi‐BICs merge to an exceptional point (EP). Around EP, one of the BICs transforms to chiral BIC with circular eigenstate polarization. In the parameter space, different elliptical eigenstate polarizations with the same helicity wind around the EP. The polarizations of the quasi‐BICs nearly fully cover the Poincaré sphere by changing the geometry parameters. The superchiral fields of the quasi‐BICs will also be greatly enhanced near the EP. The simulation result shows high circular dichroism at resonance frequency. The design provides a new strategy for polarization detection and chiral light sources. [ABSTRACT FROM AUTHOR]

Projected-search methods for bound-constrained optimization are based on performing a search along a piecewise-linear continuous path obtained by projecting a search direction onto the feasible region. A potential benefit of a projected-search method is that many changes to the active set can be made at the cost of computing a single search direction. As the objective function is not differentiable along the search path, it is not possible to use a projected-search method with a step that satisfies the Wolfe conditions, which require the directional derivative of the objective function at a point on the path. For this reason, methods based in full or in part on a simple backtracking procedure must be used to give a step that satisfies an 'Armijo-like' sufficient decrease condition. As a consequence, conventional projected-search methods are unable to exploit sophisticated safeguarded polynomial interpolation techniques that have been shown to be effective for the unconstrained case. This paper describes a new framework for the development of a general class of projected-search methods for bound-constrained optimization. At each iteration, a descent direction is computed with respect to a certain extended active set. This direction is used to specify a search direction that is used in conjunction with a step length computed by a quasi-Wolfe search. The quasi-Wolfe search is designed specifically for use with a piecewise-linear search path and is similar to a conventional Wolfe line search, except that a step is accepted under a wider range of conditions. These conditions take into consideration steps at which the restriction of the objective function on the search path is not differentiable. Standard existence and convergence results associated with a conventional Wolfe line search are extended to the quasi-Wolfe case. In addition, it is shown that under a standard nondegeneracy assumption, any method within the framework will identify the optimal active set in a finite number of iterations. Computational results are given for a specific projected-search method that uses a limited-memory quasi-Newton approximation of the Hessian. The results show that, in this context, a quasi-Wolfe search is substantially more efficient and reliable than an Armijo-like search based on simple backtracking. Comparisons with a state-of-the-art bound-constrained optimization package are also presented. [ABSTRACT FROM AUTHOR]

Quasibound states in the continuum (BIC) have earned extensive attentions due to the capability to realize extremely high quality‐factor (Q‐factor) resonance. Here, a metamaterial composed of silicon dioxide (SiO2) with low refractive index (≈1.45) on gold (Au) reflection mirror is proposed to realize narrowband perfect absorption with the assistance of quasi‐BIC and surface lattice resonance. The proposed SiO2‐Au absorber based on SiO2 metamaterial is composed of two tilted SiO2 cubes into a unit cell and periodically arranged on Au reflection mirror. By optimizing the geometry parameters, the proposed absorber presents both accidental quasi‐BIC and symmetry‐protected quasi‐BIC modes with near‐perfect absorptivity and high Q‐factor of 2330 and 1438, respectively. The Q‐factor can be further improved to 104 by increasing the thickness of SiO2 cubes to micrometer level. Meanwhile, the wavelength of absorption peak shows linear sensitivity of 16.67 and 17.88 nm per degree to incident angles as the absorptivity is higher than 92% and 75% in the spectra range of 215.0–141.0 nm, respectively. These results open the avenue for the metamaterial absorber in emitter, imaging, and biosensing applications. [ABSTRACT FROM AUTHOR]

A six-axis machining configuration is proposed to improve the surface quality and finishing efficiency of an aeroengine blisk. It flexibly enlarges the accessible interference-free space of the tool for finishing the full-shape surface, including the blade body, root, and hub surfaces. An error model for tool contact posture with respect to the kinematic axis errors is established, revealing the relationship between the kinematic deviation of the axes and resultant profile error. An improved Sobol method is applied for error sensitivity analysis to identify crucial error terms based on the quasi-Monte Carlo algorithm. In particular, an efficient error sensitivity index is proposed by combining a unified objective function to identify crucial error terms, followed by the simulations and cutting experiments for validation. As a result, the blade profile error was successfully suppressed by approximately 40 % in most. This work provides a fundamental framework for elevating the multi-axis machining accuracy of aeroengine blisk. • A six-axis machine tool has been proposed to achieve the full-shape-surface grinding on the blisk. • A constrained error sensitivity index model was proposed to compensate for key error terms. • Sensitivity analysis was conducted using an improved Sobol method incorporated quasi-Monte-Carlo algorithm. • The effectiveness of error sensitivity analysis and corresponding tool-path-based compensation were verified. [ABSTRACT FROM AUTHOR]

In order to guide the design of quasi-zero stiffness isolator with asymmetric stiffness and mismatched load based on X-shaped negative stiffness structure, the bifurcation and the chaos-occurring parameter region are investigated. The equilibrium point bifurcation with different load conditions and stiffness types is first obtained, and the invariant manifolds at specific parameters can be compared for four operating conditions based on a combination of two asymmetric stiffnesses and two mismatch loads. The displacement transmissibility and the direct current component of response are analyzed under these four operating conditions, and based on the results, it can be found that the four operating conditions can be divided into two categories, each with a similar pattern. Finally, the chaos-occurring parameter region is analyzed by means of largest Lyapunov exponent, and the maximum external excitation amplitude is used to indirectly evaluate the operation stability margin of these four operating conditions. [ABSTRACT FROM AUTHOR]

The work proves that under conditions of instability of the second derivatives of the function in the minimization region, the estimate of the convergence rate of Newton's method is determined by the parameters of the irreducible part of the conditionality degree of the problem. These parameters represent the degree of difference between eigenvalues of the matrices of the second derivatives in the coordinate system, where this difference is minimal, and the resulting estimate of the convergence rate subsequently acts as a standard. The paper studies the convergence rate of the relaxation subgradient method (RSM) with optimization of the parameters of two-rank correction of metric matrices on smooth strongly convex functions with a Lipschitz gradient without assumptions about the existence of second derivatives of the function. The considered RSM is similar in structure to quasi-Newton minimization methods. Unlike the latter, its metric matrix is not an approximation of the inverse matrix of second derivatives but is adjusted in such a way that it enables one to find the descent direction that takes the method beyond a certain neighborhood of the current minimum as a result of one-dimensional minimization along it. This means that the metric matrix enables one to turn the current gradient into a direction that is gradient-consistent with the set of gradients of some neighborhood of the current minimum. Under broad assumptions on the parameters of transformations of metric matrices, an estimate of the convergence rate of the studied RSM and an estimate of its ability to exclude removable linear background are obtained. The obtained estimates turn out to be qualitatively similar to estimates for Newton's method. In this case, the assumption of the existence of second derivatives of the function is not required. A computational experiment was carried out in which the quasi-Newton BFGS method and the subgradient method under study were compared on various types of smooth functions. The testing results indicate the effectiveness of the subgradient method in minimizing smooth functions with a high degree of conditionality of the problem and its ability to eliminate the linear background that worsens the convergence. [ABSTRACT FROM AUTHOR]

Angles-only navigation methods are compelling for distributed space systems (DSS) such as swarms and constellations. However, complex dependencies between state observability and system parameters present a challenging design problem. This paper proposes a unified angles-only observability analysis and design framework enabling designers of a DSS to 1) analytically determine whether its orbit state is observable, 2) numerically estimate its expected navigation performance, and 3) intelligently optimize the system to meet navigation requirements. First, a new system measurement topology representation is proposed for which analytic orbit observability can be assessed via a set of graphical conditions. Second, methods for numeric estimation of the achievable state covariance are augmented with auxiliary state variables, dynamics uncertainty, and measurement availability constraints. Third, a system cost function is developed and the topological and numeric methods are placed within a quasi-Newton optimization framework to enable automatic system design. The optimization is applied to a distributed science swarm and a space situational awareness constellation in lunar orbit. Both scenarios converge to a global cost minimum and output designs that achieve user requirements under realistic measurement conditions and constraints. Combined analytic and numeric methods therefore presents a powerful tool for design of angles-only DSS. [ABSTRACT FROM AUTHOR]

In order to study the effect of unbalance loading on the stiffness of rhombic negative stiffness vibration isolation system, based on the mechanical analysis method, the mathematical model of the vibration isolation system under unbalance loading was established, the dimensionless stiffness-displacement nonlinear curves were obtained, and the influence of unbalance loading on its quasi-zero stiffness characteristics was analyzed. Simulation experiments were carried out using simulink to apply excitation to the vibration base of the vibration isolation system under unbalance loading, and the time-varying stiffness of the vibration isolation system under different excitations was obtained. Combined with Fourier transform, the time-varying and amplitude-frequency characteristics of the stiffness of the vibration isolation system were discussed. The results show that the higher the unbalance loading, the narrower the low stiffness interval and the weaker the quasi-zero stiffness characteristic. The fluctuation range and peak value of the time-varying stiffness increase larger with the increase of unbalance loading, but the fluctuation trend of the time-varying stiffness is not affected by unbalance loading. The amplitude of the time-varying stiffness is mainly concentrated in the low-frequency interval, which decreases with the increase of the frequency, and eventually approaches 0. Stiffness of the vibration isolation system will be influenced by unbalance loading. [ABSTRACT FROM AUTHOR]

This paper studies the quasi-maximum likelihood estimator (quasi-MLE) of a change point in variance for the fractionally integrated noise with memory parameter d ∈ (- 0.5 , 0.5) , and the asymptotic behaviors of the estimator are examined. We show that: (1) For the case of fixed break magnitude, the quasi-MLE of the change point is inconsistent, while that of the change-point fraction is T-consistent. (2) For the case of shrinking break magnitude, the intermediate memory dependency has no impact on the convergence rate of the quasi-MLE of the change point. However, it is not the case when the process is long-range dependent. Specifically, the asymptotic behaviors of the quasi-MLE of the change point vary from the case where 0 < d < 0.25 to the cases where d = 0.25 and 0.25 < d < 0.5 , and the phase transition occurs when d = 0.25 . In addition, the quasi-MLEs of the pre-variance and post-variance are both examined, and we show that they are consistent for both fixed and shrinking break magnitude. Monte Carlo simulations and an empirical study are conducted to illustrate the theoretical results on finite-sample performance. [ABSTRACT FROM AUTHOR]

This work introduces a novel isogeometric method for addressing steady, saturated groundwater flow as a free-boundary problem. The innovation lies in adopting a double spline parameterization technique for accurately representing both the porous medium and the fully saturated zone. To linearise the governing equation, we differentiate them with respect to the coefficients of the geometric parameterization. This process results in a quasi-Newton method. Several benchmark numerical tests demonstrate the applicability and effectiveness of the proposed technique. [ABSTRACT FROM AUTHOR]

We obtain results on the existence and approximation of fixed points of enriched contractions in quasi-Banach spaces and thus extend the previous results for enriched contractions defined on Banach spaces [Berinde, V.; Păcurar, M. Approximating fixed points of enriched contractions in Banach spaces. J. Fixed Point Theory Appl. 22 (2020), no. 2, Paper No. 38, 10 pp.]. The theoretical results are illustrated by means of an appropriate example of enriched contraction on a quasi-Banach space which is not a Banach space and thus show that our new results are effective generalizations of the previous ones in literature. [ABSTRACT FROM AUTHOR]

Summary: This paper proposes a new extendable multicell topology based on the conventional quasi‐Z‐source converter (QZSC). The proposed topology has a multicell scheme and employs an active switched capacitor/inductor (ASC/SL) network. Therefore, it is entitled extended multicell ASC/SL QZSC (EMc‐ASC/SL‐QZSC). The proposed topology is augmented by cascading a modular cell consisting of two capacitors, an inductor, and a diode. The EMc‐ASC/SL‐QZSC offers significant advantages over existing QZSC‐based configurations. It has a high boosting capability that results in a wider output voltage range while simultaneously reducing voltage stress on capacitors and switching devices, all without losing voltage gain. Furthermore, this topology effectively reduces input current ripple, which contributes to a smoother charging current profile for capacitors, reducing electromagnetic interference (EMI) and improving overall efficiency. The practicality and performance of the EMc‐ASC/SL‐QZSC topology are comprehensively assessed through extensive numerical simulations and experimental verification, utilizing a laboratory‐built prototype. [ABSTRACT FROM AUTHOR]

Summary: Quasi‐Newton iterations are constructed for the finite element solution of small‐strain nonlinear elasticity systems in 3D. The linearizations are based on spectral equivalence and hence considered as variable preconditioners arising from proper simplifications in the differential operator. Convergence is proved, providing bounds uniformly w.r.t. the FEM discretization. Convenient iterative solvers for linearized systems are also proposed. Numerical experiments in 3D confirm that the suggested quasi‐Newton methods are competitive with Newton's method. [ABSTRACT FROM AUTHOR]

Context: This project performed quantum chemical computation, through kinetic and thermodynamic analyses to compare relative reactivity, reaction rate, and equilibrium composition from the possible pathways in connection with stabilizer-nitrodioxide reactions to determine the stability of the materials for practical application. Corresponding achievements have promoted the use of N-methyl-p-nitroaniline (MNA) and dinitrophenyl malonamide series (M3, M4, and M5) stabilizers as high priorities for selection. Methods: The Gaussian 09 program (G09) (Frisch et al 2009) and density functional theory (DFT) calculations with the B3LYP/6-31G(d,p) function were performed to obtain related geometric and thermodynamic energy data for the molecular systems in this study. The synchronous transit-guided quasi-Newton method (STQN) (Peng and Schlegel Isr J Chem 33:49, 1993) was applied through the QST3 procedure to identify single imaginary frequency-valued transition-state species. The related reaction rate constant (k) and pre-exponential factor (A) were obtained, based on transition state theory (Su 2008), using Eqs. 11 and 12. [ABSTRACT FROM AUTHOR]

Summary: We analyze the convergence of quasi‐Newton methods in exact and finite precision arithmetic using three different techniques. We derive an upper bound for the stagnation level and we show that any sufficiently exact quasi‐Newton method will converge quadratically until stagnation. In the absence of sufficient accuracy, we are likely to retain rapid linear convergence. We confirm our analysis by computing square roots and solving bond constraint equations in the context of molecular dynamics. In particular, we apply both a symmetric variant and Forsgren's variant of the simplified Newton method. This work has implications for the implementation of quasi‐Newton methods regardless of the scale of the calculation or the machine. [ABSTRACT FROM AUTHOR]

Summary: The present article proposes a partitioned Dirichlet‐Neumann algorithm, that allows to address unique challenges arising from a novel mixed‐dimensional coupling of very slender fibers embedded in fluid flow using a regularized mortar‐type finite element discretization. The fibers are modeled via one‐dimensional (1D) partial differential equations based on geometrically exact nonlinear beam theory, while the flow is described by the three‐dimensional (3D) incompressible Navier‐Stokes equations. The arising truly mixed‐dimensional 1D‐3D coupling scheme constitutes a novel approximate model and numerical strategy, that naturally necessitates specifically tailored solution schemes to ensure an accurate and efficient computational treatment. In particular, we present a strongly coupled partitioned solution algorithm based on a Quasi‐Newton method for applications involving fibers with high slenderness ratios that usually present a challenge with regard to the well‐known added mass effect. The influence of all employed algorithmic and numerical parameters, namely the applied acceleration technique, the employed constraint regularization parameter as well as shape functions, on efficiency and results of the solution procedure is studied through appropriate examples. Finally, the convergence of the two‐way coupled mixed‐dimensional problem solution under uniform mesh refinement is demonstrated, a comparison to a 3D reference solution is performed, and the method's capabilities in capturing flow phenomena at large geometric scale separation is illustrated by the example of a submersed vegetation canopy. [ABSTRACT FROM AUTHOR]

An effective and precise physical model is generally required for the performance assessment of reinforced concrete (RC) components. In this study, a convergence‐enhanced Timoshenko beam element considering finite deformation is proposed for the stochastic nonlinear analysis of RC components. The unified framework of the rank 2 correction matrix is obtained by approximating the iterative matrix through the linearly independent basis vectors, and two types of Broyden–Fletcher–Goldfarb–Shanno (BFGS) operators are constructed. Then, a consistent solution scheme with superior numerical stability and efficiency is proposed based on the second kind of BFGS operator and improved quasi‐Newton method. Accurate discretization of the displacement fields and description of nonlinear sectional behavior are achieved by the high‐order Lagrangian interpolation functions, concrete damage‐plasticity model and J2 plasticity model. In an updated Lagrangian formulation, these shape functions and constitutive relationships are used to develop a complete secant stiffness with higher‐order terms in the strain tensor and residual force vector. To validate the proposed Timoshenko beam element, numerical applications involving material nonlinearity and geometrical nonlinearity are conducted. The numerical stability and efficiency of the solution scheme, the shear‐locking free technique, and the oscillation of axial force are thoroughly examined and discussed by solution of RC columns, cantilever beam and progressive collapse of planar RC frame. Finally, the parametric study considering the geometric and material randomness indicates that the RC column designed for flexural failure mode suffered considerable degradation of loading capacity and a larger scatter of residual load. [ABSTRACT FROM AUTHOR]

For the generalized Sturm–Liouville problem (GSLP), a new formulation is undertaken to reduce the number of unknowns from two to one in the target equation for the determination of eigenvalue. The eigenparameter-dependent shape functions are derived for using in a variable transformation, such that the GSLP becomes an initial value problem for a new variable. For the uniqueness of eigenfunction an extra condition is imposed, which renders the right-end value of the new variable available; a derived implicit nonlinear equation is solved by an iterative method without using the differential; we can achieve highly precise eigenvalues. For the nonlocal Sturm–Liouville problem (NSLP), we consider two types of integral boundary conditions on the right end. For the first type of NSLP we can prove sufficient conditions for the positiveness of the eigenvalue. Negative eigenvalues and multiple solutions may exist for the second type of NSLP. We propose a boundary shape function method, a two-dimensional fixed-quasi-Newton method and a combination of them to solve the NSLP with fast convergence and high accuracy. From the aspect of numerical analysis the initial value problem of ordinary differential equations and scalar nonlinear equations are more easily treated than the original GSLP and NSLP, which is the main novelty of the paper to provide the mathematically equivalent and simpler mediums to determine the eigenvalues and eigenfunctions. [ABSTRACT FROM AUTHOR]

The BFGS method is a common and effective method for solving unconstrained optimization problems in quasi-Newton algorithm. However, many scholars have proven that the algorithm may fail in some cases for nonconvex problems under Wolfe conditions. In this paper, an adaptive projection BFGS algorithm is proposed naturally which can solve nonconvex problems, and the following properties are shown in this algorithm: ➀ The generation of the step size α j satisfies the popular Wolfe conditions; ➁ a specific condition is proposed which has sufficient descent property, and if the current point satisfies this condition, the ordinary BFGS iteration process proceeds as usual; ➂ otherwise, the next iteration point x j + 1 is generated by the proposed adaptive projection method. This algorithm is globally convergent for nonconvex problems under the weak-Wolfe-Powell (WWP) conditions and has a superlinear convergence rate, which can be regarded as an extension of projection BFGS method proposed by Yuan et al. (J. Comput. Appl. Math. 327:274-294, 2018). Furthermore, the final numerical results and the application of the algorithm to the Muskingum model demonstrate the feasibility and competitiveness of the algorithm. [ABSTRACT FROM AUTHOR]