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This paper considers the regularization continuation method and the trust-region updating strategy for the optimization problem with linear equality constraints.The proposed method utilizes the linear conservation law of the regularization continuation method such that it does not need to compute the correction step for preserving the feasibility other than the previous continuation methods and the quasi-Newton updating formulas for the linearly constrained optimization problem. Moreover, the new method uses the special limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) formula as the preconditioning technique to improve its computational efficiency in the well-posed phase, and it uses the inverse of the regularized two-sided projection of the Lagrangian Hessian as the pre-conditioner to improve its robustness. Numerical results also show that the new method is more robust and faster than the traditional optimization method such as the alternating direction method of multipliers (ADMM),the sequential quadratic programming (SQP) method (the built-in subroutine fmincon.m of the MATLAB2020a environment), and the recent continuation method (Ptctr). The computational time of the new method is about 1/3 of that of SQP (fmincon.m). Finally, the global convergence analysis of the new method is also given., Comment: arXiv admin note: substantial text overlap with arXiv:2101.07055, arXiv:2012.14808

A simple and practical Cs2CO3-promoted method for the synthesis of 6-nitroindole derivatives from enaminones and nitroaromatic compounds has been developed.

An efficient defluorinative net-[3 + 3]-cyclization strategy for the construction of perfluoroalkyl-substituted pyrimidine derivatives by using a series of perfluoroalkyl alkynes and amidines as starting materials was developed. The present reaction proceeded successfully under transition-metal-free conditions to form two new C–N bonds and a new heterocyclic ring through a sequence of hydroamination, defluorination, and annulation. The desired pyrimidines could be obtained with good functional group tolerance and moderate to good yields. Moreover, the distinctive fluorine effects of perfluoroalkyl substituents are vital for tuning the reactivity of alkynes for the anticipated defluorinative annulation. The pendant π system would lower associated bond dissociation energy significantly compared to that of a nonactivated C(sp3)–F bond.

The global minimum point of an optimization problem is of interest in engineering fields and it is difficult to be solved, especially for a nonconvex large-scale optimization problem. In this article, we consider a new memetic algorithm for this problem. That is to say, we use the continuation Newton method with the deflation technique to find multiple stationary points of the objective function and use those found stationary points as the initial seeds of the evolutionary algorithm, other than the random initial seeds of the known evolutionary algorithms. Meanwhile, in order to retain the usability of the derivative-free method and the fast convergence of the gradient-based method, we use the automatic differentiation technique to compute the gradient and replace the Hessian matrix with its finite difference approximation. Accordingto our numerical experiments, this new algorithm works well for unconstrained optimization problems and finds their global minima efficiently, in comparison to the other representative global optimization methods such as the multi-start methods (the built-in subroutine GlobalSearch.m of MATLAB R2021b, GLODS and VRBBO), the branch-and-bound method (Couenne, a state-of-the-art open-source solver for mixed integer nonlinear programming problems), and the derivative-free algorithms (CMA-ES and MCS). Mathematics Subject Classification (2010) 65K05 · 65L05 · 65L20

A straightforward aerobic oxidative esterification of aryl aldehydes with alcohols has been developed for the synthesis of substituted esters by employing vitamin B1 as a cost-effective, metal-free, and eco-friendly NHC catalyst. Air is used as a green terminal oxidant. The reaction is a useful addition to the existing NHC-catalytic oxidative esterification.

Efficient synthesis of fluoroalkylated tri(hetero)arylphosphine oxides from perfluoroalkyl ketones and phosphine oxides or phosphonates has been achieved via successive C(sp3)–F bond activation under mild reaction conditions. This approach involving new C(sp2)–P/C(sp2)–O bond formation and fluoroalkylated heterocycle construction distinguishes itself by its broad substrate scope and synthetic simplicity. Moreover, tri(hetero)arylphosphines could also be prepared in high yields by further reductive transformation.

This paper considers the generalized continuation Newton method and thetrust-region updating strategy for the underdetermined system of nonlinear equations. Moreover, in order to improve its computational efficiency, the new method will not update the Jacobian matrix when the current Jacobian matrix performs well. The numerical results show that the new method is more robust and faster than the traditional optimization method such as the Levenberg-Marquardt method (a variant of trust-region methods, the built-in subroutine fsolve.m of the MATLAB R2020a environment). The computational time of the new method is about 1/8 to 1/50 of that of fsolve. Furthermore, it also proves the global convergence and the local superlinear convergence of the new method under some standard assumptions., arXiv admin note: text overlap with arXiv:2006.02634, arXiv:2006.07568

A three-component [3 + 2 + 1] annulation strategy for the synthesis of biologically and pharmaceutically active 2,3-diarylpyridine derivatives by using a series of allylic alcohols, ketones, and ammonium acetate as substrates has been developed. The method proceeds efficiently under metal-free conditions, and the desired heterocycles could be obtained in a site-specific selectivity manner with good functional group tolerance.

This paper considers an explicit continuation method and the trust-region updating strategy for the unconstrained optimization problem. Moreover, in order to improve its computational efficiency and robustness, the new method uses the switching preconditioning technique. In the well-conditioned phase, the new method uses the L-BFGS method as the preconditioning technique in order to improve its computational efficiency. Otherwise, the new method uses the inverse of the Hessian matrix as the pre-conditioner in order to improve its robustness. Numerical results also show that the new method is more robust and faster than the traditional optimization method such as the trust-region method and the line search method. The computational time of the new method is about one percent of that of the trust-region method (the subroutine fminunc.m of the MATLAB2019a environment is set by the trust-region method) or one fifth of that of the line search method (fminunc.m is set by the quasi-Newton method) for the large-scale problem. Finally, the global convergence analysis of the new method is also given.

International audience; Dendritic cells (DCs) are mononuclear phagocytes that are specialized in the induction and functional polarization of effector lymphocytes, thus orchestrating immune defenses against infections and cancer. The population of DC encompasses distinct cell types that vary in their efficacy for complementary functions and are thus likely involved in defending the body against different threats. Plasmacytoid DCs specialize in the production of high levels of the antiviral cytokines type I interferons. Type 1 conventional DCs (cDC1s) excel in the activation of cytotoxic CD8 + T cells (CTLs) which are critical for defense against cancer and infections by intracellular pathogens. Type 2 conventional DCs (cDC2s) prime helper CD4 + T cells for the production of type 2 cytokines underpinning immune defenses against worms or of IL-17 promoting control of infections by extracellular bacteria or fungi. Hence, clinically manipulating the development and functions of DC types could have a major impact for improving treatments against many diseases. However, the rarity and fragility of human DC types is impeding advancement towards this goal. To overcome this roadblock, major efforts are ongoing to generate in vitro large numbers of distinct human DC types. We review here the current state of this research field, emphasizing recent breakthrough and proposing future priorities. We also pinpoint the necessity to develop a consensus nomenclature and rigorous methodologies to ensure proper identification and characterization of human DC types. Finally, we elaborate on how faithful in vitro models of human DC types can accelerate our understanding of the biology of these cells and the engineering of next generation vaccines or immunotherapies against viral infections or cancer.

For nonlinear equations, the homotopy methods (continuation methods) are popular in engineering fields since their convergence regions are large and they are quite reliable to find a solution. The disadvantage of the classical homotopy methods is that their computational time is heavy since they need to solve many auxiliary nonlinear systems during the intermediate continuation processes. In order to overcome this shortcoming, we consider the special explicit continuation Newton method with the residual trust-region time-stepping scheme for this problem. According to our numerical experiments, the new method is more robust and faster to find the required solution of the real-world problem than the traditional optimization method (the built-in subroutine fsolve.m of the MATLAB environment) and the homotopy continuation methods(HOMPACK90 and NAClab). Furthermore, we analyze the global convergence and the local superlinear convergence of the new method.

The nonlinear optimization problem with linear constraints has many applications in engineering fields such as the visual-inertial navigation and localization of an unmanned aerial vehicle maintaining the horizontal flight. In order to solve this practical problem efficiently, this paper constructs a continuation method with the trusty time-stepping scheme for the linearly equality-constrained optimization problem at every sampling time. At every iteration, the new method only solves a system of linear equations other than the traditional optimization method such as the sequential quadratic programming (SQP) method, which needs to solve a quadratic programming subproblem. Consequently, the new method can save much more computational time than SQP. Numerical results show that the new method works well for this problem and its consumed time is about one fifth of that of SQP (the built-in subroutine fmincon.m of the MATLAB2018a environment) or that of the traditional dynamical method (the built-in subroutine ode15s.m of the MATLAB2018a environment). Furthermore, we also give the global convergence analysis of the new method.

In this paper, a method of improving vertical positioning accuracy with the global positioning system information and barometric pressure values is proposed. Firstly, we clear null values for the raw data collected in various environments, and use the 3 $$\sigma$$ -rule to identify outliers. Secondly, the weighted multinomial logistic regression (WMLR) classifier is trained to obtain the predicted altitude of outliers. Finally, in order to verify its effect, we compare the multinomial logistic regression (MLR) method, the WMLR method, and the support vector machine (SVM) method for the cleaned dataset which is regarded as the test baseline. The numerical results show that the vertical positioning accuracy is improved from 5.9 m (the MLR method), 5.4 m (the SVM method) to 5 m (the WMLR method) for 67% test points.

With the continuous development of intelligent terminal technology, the demand for Location Based Services (LBS) is also increased. Thus, the research of indoor positioning technology is of great significance. Based on the characteristic of the mobile positioning terminal and the presence of the AP in the indoor positioning environment, the indoor location fingerprint algorithm is the most feasible method due to its stable performance without the need for additional hardware. However, the traditional methods do not take the weight of the composition into consideration, which actually affects the precision of positioning much. In this paper, an improved algorithm based on weighted K-nearest neighbors (W-KNN) is proposed. In the off-line stage, the algorithm filters out invalid data by using data expectation, and selects the mean of RSS and the variance of access points (APs) as the eigenvector. In the on-line stage, according to the variance of APs, the weighted distance is proposed to calculate the similarity. Meanwhile, the nearest main neighbor and (K-1) auxiliary neighbors are obtained by comparing the weighted distance. Using the correlation between main neighbor and (K-1) auxiliary neighbors, the location is derived. Experimental results show that the precision of the proposed algorithm is better than that of using the RSSI location fingerprinting algorithm alone in the indoor environment.

With the fast development of Location Based Service (LBS) applications in recent years, the demands for accurate indoor localization techniques have attracted significant attention and risen rapidly. Among all the techniques, due to its stable performance without the need for additional hardware, the RSS-based fingerprinting localization is the most viable method. However, the traditional methods do not make full use of the energy-based model, which actually affects the accuracy of positioning a lot. In this paper, an improved probabilistic localization algorithm named Weighted Restricted Boltzmann Machine (WRBM) is proposed, which takes the energy-based model into consideration. By calculating the related probabilistic function, the proposed algorithm gets higher accuracy. As shown in the experimental results, the proposed algorithm performs much better than the other typical fingerprinting localization methods.

This article gives a new method based on the dynamical system of differential-algebraic equations for the smallest eigenvalue problem of a symmetric matrix. First, the smallest eigenvalue problem is converted into an equivalent constrained optimization problem. Second, from the Karush–Kuhn–Tucker conditions for this special equality-constrained problem, a special continuous dynamical system of differential-algebraic equations is obtained. Lastly, based on the implicit Euler method and an analogous trust-region technique, we obtain a prediction-correction method to compute a steady-state solution of this special system of differential-algebraic equations, and consequently obtain the smallest eigenvalue of the original problem. We also analyze the local superlinear property for this new method, and present the promising numerical results, in comparison with other methods.

In this article, we investigate some theoretical and computational issues of the geometric buildup algorithm proposed by Sit, Wu and Yuan (Bull. Math. Biol. 71:1914–1933, 2009) for the solution of the distance geometry problem with sparse and inexact distances. This algorithm repeatedly uses a least-squares approximation to determine the position of an undetermined atom, using the distances from this atom to a set of previously determined ones. The least-squares approximation, obtained from the singular value decomposition of a distance-induced matrix, can find the best possible position for the atom, even if the distances have small errors, as they usually do in practice, and therefore make the geometric buildup algorithm more stable than its previous versions that relied on linear system solvers. We estimate its numerical errors and prove some of its key mathematical properties. We also present some numerical results with varying some of the parameters in the algorithm and show how they may be used to improve its performance and computational accuracy.

Problem statement: There is a large demand for wireless Location-Based Service (LBS) and it is provided by many wireless cellular systems. In process of positioning a Mobile Station (MS), the computing speed is as important as the positioning accuracy and the algorithm should also be resistant to environmental influences. Approach: A new positioning method based on Weighted Centroid Correction Localization (WCCL) for wireless cellular systems is introduced in this article. Firstly, referring to the receiving-state of an MS in cellular systems, it computes a weighted centroid of surrounding Base Stations (BSs) as a rough approximate position of the MS. Then, according to the distances between the MS and the BSs being less or bigger than the computed distances between the BSs and the weighted centroid, it corrects the coordinate of the weighted centroid towards the directions of the BSs by moving it closer or farther in turn. Results: According to our experiments, WCCL improves the positioning accuracy, as well as to provide a better resistance to environmental influences. Conclusion: As a modified centroid-based localization algorithm, WCCL obtains weighting factors from the receiving-state of MS in multi-cells structured cellular systems and obtains a better positioning result in cellular systems without updating the network equipment. Therefore, for the cellular positioning problem, WCCL algorithm can be an alternate solution.

This article gives a second pseudo-transient method for a special system of nonlinear equations, which arises from chemical reaction rate equations. This method uses a special second-order Rosenbrock method as the discrete difference scheme, which satisfies a linear conservation law. Moreover, it adaptively adjusts the time step in inverse proportion to an arithmetic mean of the current residual and the previous residual at every iteration step. For a singular system of nonlinear equations, under some standard assumptions, local convergence of the new method is addressed. Finally, some promise numerical results are also reported.

Recently, a continuous method has been proposed by Golub and Liao as an alternative way to solve the minimum and interior eigenvalue problems. According to their numerical results, their method seems promising. This article is an extension along this line. In this article, firstly, we convert an eigenvalue problem to an equivalent constrained optimization problem. Secondly, using the Karush–Kuhn–Tucker conditions of this equivalent optimization problem, we obtain a variant of the Rayleigh quotient gradient flow, which is formulated by a system of differential-algebraic equations. Thirdly, based on the Rayleigh quotient gradient flow, we give a practical numerical method for the minimum and interior eigenvalue problems. Finally, we also give some numerical experiments of our method, the Golub and Liao method, and EIGS (a Matlab implementation for computing eigenvalues using restarted Arnoldi’s method) for some typical eigenvalue problems. Our numerical experiments indicate that our method seems promising for most test problems.

This article gives a trajectory-following method for the steady state of chemical reaction rate equations. In order to avoid wasting unnecessary computing time during the steady-state phase and get roughly accurate solutions during the transient-state phase, this method is realized via adopting the semi-implicit Euler formula as the stepping direction and adaptively adjusting the time-step size by an analogous trust-region technique. Under some standard assumptions, its global convergence analysis and local superlinear convergence analysis are also given. Finally, some numerical experiments of this method, in comparison with the traditional optimization methods and ordinary differential equation methods, are reported. The numerical results show that this trajectory-following method is a promising solution for this class of problems.

Rosenbrock methods are popular for solving a stiff initial-value problem of ordinary differential equations. One advantage is that there is no need to solve a nonlinear equation at every iteration, as compared with other implicit methods such as backward difference formulas or implicit Runge–Kutta methods. In this article, we introduce a trust-region technique to select the time steps of a second-order Rosenbrock method for a special initial-value problem, namely, a gradient system obtained from an unconstrained optimization problem. The technique is different from the local error approach. Both local and global convergence properties of the new method for solving an equilibrium point of the gradient system are addressed. Finally, some promising numerical results are also presented.

The Levenberg-Marquardt method is a popular method for both optimization problems and equilibrium problems in dynamical systems. In this article, we study the convergence properties of the Levenberg-Marquardt method with the standard matrix update scheme. In our global convergence proof, we relax the condition that update matrices be bounded, and only require that their norms increase at most linearly. Furthermore, we analyze its local convergence for the uniformly convex function. In this case, the Levenberg-Marquardt method has superlinear convergence, and the initial matrix can be chosen arbitrarily for the Broyden-Fletcher-Goldfarb-Shanno (BFGS) formula.

A new 3D fingerprinting positioning scheme based on cellular networks is proposed by using implicit information of the location around geographic environments. Compared with original fingerprint positioning scheme, singular measurement is processed at the beginning of the proposed scheme. The main improvement of our proposed scheme is to employ cell matching degree and choose the best reasonable fingerprint according to the correlation of its surrounding points. Additionally, in order to improve searching efficiency, a new searching window is introduced. Finally, compared with the maximum likelihood method and the weighted K nearest neighbors method, the promising numerical results are also presented.

In order to reduce the number of unnecessary UE (User Equipment) cell reselection in Multi-RAT (Multi-Radio Access Technology) that consists of 2G, 3G and LTE for energy saving, a new method on procedure of cell reselection according to UE preference based on priority level is proposed in this paper. Later, this method will impact the measurement action and UE energy saving. The simulation results prove that the proposed scheme shows significant performance improvement on reducing the number of cell reselection and also UE power consumption.

This paper gives a new prediction-correction method based on the dynamical system of differential-algebraic equations for the smallest generalized eigenvalue problem. First, the smallest generalized eigenvalue problem is converted into an equivalent-constrained optimization problem. Second, according to the Karush-Kuhn-Tucker conditions of this special equality-constrained problem, a special continuous dynamical system of differential-algebraic equations is obtained. Third, based on the implicit Euler method and an analogous trust-region technique, a prediction-correction method is constructed to follow this system of differential-algebraic equations to compute its steady-state solution. Consequently, the smallest generalized eigenvalue of the original problem is obtained. The local superlinear convergence property for this new algorithm is also established. Finally, in comparison with other methods, some promising numerical experiments are presented.

In this paper we provide a thorough analysis of the inter-cell interference coordination in the heterogeneous LTE-Advanced system. With the introduction of Het-net (heterogeneous networks) deployments, more serious interference will impact the Rx-Tx time difference measurement at UE side to deteriorate the positioning accuracy. We present an inter-cell interference coordination method using the ABS (almost blank sub-frames) as a novel time domain solution. Our simulation results show that the proposed method can satisfy the 3GPP rel-9 UE Rx-Tx time difference measurement accuracy requirement in Het-net scenarios.

The Observed Time Difference of Arrival (OTDOA) as a major positioning method in 3rd Generation Partnership Project (3GPP) specification has been deeply researched in Long Term Evolution Advanced (LTE-A) system. This paper analyzes the new interference scenarios in Heterogeneous Network (Het-Net) and the drawbacks of conventional OTDOA method which are caused by LPN (Low Power Nodes) deployed in Het-Net. In this paper, we propose a Time division multiplex (TDM) and a Code division multiplex (CDM) scheme for positioning reference signal (PRS) transmitting to solve these problems in Het-Net. Simulation results show that the proposed scheme can greatly improve the positioning accuracy compared with the conventional method and its performance meets the Federal communication commission (FCC) requirement.

Wireless sensor networks (WSNs) consist of a large number of low-cost miniature sensors, which can be applied to battlefield surveillance, environmental monitoring, target tracking, and other applications related to the positions of sensors. The location information of sensors is of great importance for wireless sensor networks. In this paper, we propose a new localization algorithm for the wireless sensor network based on time difference of arrival (TDOA), which is a typical algorithm in the wireless localization field. In order to improve the localization accuracy of a sensor, a new strategy is proposed for a localized sensor being upgraded to an anchor node, which is used to localize the position of the next sensor. Performance analysis and simulation results show that the revised TODA localization algorithm has the higher localization accuracy when compared with the original TDOA location method.