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Inspired by the first-order method of Malitsky and Pock, we propose a new variational framework for compressed MR image reconstruction which introduces the application of a rotation-invariant discretization of total variation functional into MR imaging while exploiting BM3D frame as a sparsifying transform. In the first step, we provide theoretical and numerical analysis establishing the exceptional rotation-invariance property of this total variation functional and observe its superiority over other well-known variational regularization terms in both upright and rotated imaging setups. Thereupon, the proposed MRI reconstruction model is presented as a constrained optimization problem, however, we do not use conventional ADMM-type algorithms designed for constrained problems to obtain a solution, but rather we tailor the linesearch-equipped method of Malitsky and Pock to our model, which was originally proposed for unconstrained problems. As attested by numerical experiments, this framework significantly outperforms various state-of-the-art algorithms from variational methods to adaptive and learning approaches and in particular, it eliminates the stagnating behavior of a previous work on BM3D-MRI which compromised the solution beyond a certain iteration. [ABSTRACT FROM AUTHOR]

For the structured systems of linear equations arising from the Galerkin finite element discretizations of elliptic PDE-constrained optimization problems, some preconditioners are proposed to accelerate the convergence rate of Krylov subspace methods such as GMRES for both cases of the Tikhonov parameter β not very small (equal or greater than 1e−6) and sufficiently small (less than 1e−6), respectively. We derive the explicit expressions for the eigenvalues and eigenvectors of the corresponding preconditioned matrices. Numerical results show that the corresponding preconditioned GMRES methods perform and match well with the theoretical results. [ABSTRACT FROM AUTHOR]

In this article, we focus on mobile wellness and health-related applications from the perspective of the level of imprecision present in the data used in the recommendation systems. We propose a general fuzzy optimization model based on chanced constrained optimization to design recommendation systems that can take into consideration (i) the imprecision in the data and (ii) the imprecision by which one can estimate the effect of a recommendation on the user of the system. Our proposal is one of the first to use fuzzy optimization models in health-related decision making problems and the first to define a chance constrained optimization problem for interval-valued fuzzy numbers. The proposed approach identifies a set of actions to be taken by the users in order to optimize general health-related and/or wellness condition of the user from various perspectives. The model is illustrated through the example of walking speed optimization, with an additional numerical experiment offering a comparison with traditional methods. [ABSTRACT FROM AUTHOR]

In this paper, we present a QP-free algorithm without a penalty function or a filter for nonlinear general-constrained optimization. At each iteration, three systems of linear equations with the same coefficient matrix are solved to yield search direction; the nonmonotone line search ensures that the objective function or constraint violation function is sufficiently reduced. There is no feasibility restoration phase in our algorithm, which is necessary for filter methods. The algorithm possesses global convergence as well as superlinear convergence under some mild conditions including a weaker assumption of positive definiteness. Finally, some preliminary numerical results are reported. [ABSTRACT FROM AUTHOR]

This paper deals with the numerical investigation of nonlinear optimal control problems with multiple delays in which the state trajectory and control input are subject to mixed state-control constraints. A direct approach based on a hybrid of block-pulse functions and Lagrange interpolation is proposed. The constrained optimal control problem is first reformulated as an unconstrained optimization one using a penalty function technique. The resulting optimization problem is then solved by means of the Lagrange multipliers procedure. The proposed framework is an extension and also a modification of the conventional Lagrange interpolation. Combining block-pulse functions and Lagrange interpolation allows one to simultaneously make use the advantages of the two mentioned bases. The operational matrices of delay and derivative associated with the hybrid functions are presented. An upper error bound for the proposed hybrid functions with respect to the maximum norm is obtained. Simulation studies are provided to verify the validity and reliability of the developed procedure. [ABSTRACT FROM AUTHOR]

In this paper, using an optimize-then-discretize approach, we address the numerical solution of two Fraction Partial Differential Equation constrained optimization problems: the Fractional Advection Dispersion Equation (FADE) and the two-dimensional semilinear Riesz Space Fractional Diffusion equation . Both a theoretical and experimental analysis of the problem is carried out. The algorithmic framework is based on the L-BFGS method coupled with a Krylov subspace solver. A suitable preconditioning strategy by approximate inverses is taken into account. Graphics Processing Unit (GPU) accelerator is used in the construction of the preconditioners. The numerical experiments are performed with benchmarked software/libraries enforcing the reproducibility of the results. [ABSTRACT FROM AUTHOR]

The design of a propeller for a high-speed craft is addressed by using a multi-objective numerical optimization approach. By combining a fast and reliable Boundary Elements Method (BEM), a viscous flow solver based on the RANSE approximation, a parametric 3D description of the blade and a genetic algorithm, the new propeller shape is designed to improve the propulsive efficiency, reduce the cavitation extension, increase the cavitation inception speed and maximize, at the same time, the ship speed. Rather than by constraining the propeller delivered thrust, indeed, the proposed procedure works together with an engine-propeller matching algorithm that, each time a new propeller is defined, identifies the achievable maximum ship speed and the resulting engine functioning point that turn in additional goals for the multi-objective optimization. A set of optimal propellers, obtained through the design by optimization based on potential flow calculations (via the Boundary Elements Method), are selected for additional viscous analyses (RANSE calculations) in order to further validate the results of the BEM calculations and provide a deeper insight into the complex flow fields of high speed propellers. Among this subset of optimal configurations, a final geometry is selected to verify the reliability of the design procedure by means of dedicated cavitation tunnel tests and full-scale measurements on a high-speed craft provided by Azimut|Benetti. [ABSTRACT FROM AUTHOR]

This paper presents a new powerful nature-inspired method named Virus Colony Search (VCS). VCS simulates diffusion and infection strategies for the host cells adopted by virus to survive and propagate in the cell environment. With the strategies, the individual in the new algorithm explores and exploits the search space more efficiently. To verify the performance of our VCS, both the unconstrained classic and CEC2014 modern benchmark functions, and constrained engineering design optimization problems are employed. The experimental results, considering both convergence and accuracy simultaneously, demonstrate the effectiveness of VCS for global numerical and engineering optimization problems. [ABSTRACT FROM AUTHOR]

A trust-region algorithm in association with line search filter technique for solving nonlinear equality constrained programming is proposed in this paper. In the current iteration, the trial step providing sufficient descent is generated by solving a corresponding trust-region subproblem. Then, the step size is decided by backtracking line search together with filter technique to obtain the next iteration point. The advantage of this method is that resolving trust-region subproblem many times to determine a new iteration point in traditional trust-region method can be avoided and hence the expensive computation can be lessened. And the difficult decisions in regard to the choice of penalty parameters in the merit functions can be avoided by using filter technique. Second order correction steps are introduced in the proposed algorithm to overcome Maratos effect. Convergence analysis shows that fast local convergence can be achieved under some mild assumptions. The preliminary numerical results are reported. [ABSTRACT FROM AUTHOR]

Inexact Restoration methods have been proved to be effective to solve constrained optimization problems in which some structure of the feasible set induces a natural way of recovering feasibility from arbitrary infeasible points. Sometimes natural ways of dealing with minimization over tangent approximations of the feasible set are also employed. A recent paper [Banihashemi and Kaya (2013)] suggests that the Inexact Restoration approach can be competitive with well-established nonlinear programming solvers when applied to certain control problems without any problem-oriented procedure for restoring feasibility. This result motivated us to revisit the idea of designing general-purpose Inexact Restoration methods, especially for large-scale problems. In this paper we introduce affordable algorithms of Inexact Restoration type for solving arbitrary nonlinear programming problems and we perform the first experiments that aim to assess their reliability. Initially, we define a purely local Inexact Restoration algorithm with quadratic convergence. Then, we modify the local algorithm in order to increase the chances of success of both the restoration and the optimization phase. This hybrid algorithm is intermediate between the local algorithm and a globally convergent one for which, under suitable assumptions, convergence to KKT points can be proved. [ABSTRACT FROM AUTHOR]

This paper presents a one-layer neural network to solve nonsmooth convex optimization problems based on the Tikhonov regularization method. Firstly, it is shown that the optimal solution of the original problem can be approximated by the optimal solution of a strongly convex optimization problems. Then, it is proved that for any initial point, the state of the proposed neural network enters the equality feasible region in finite time, and is globally convergent to the unique optimal solution of the related strongly convex optimization problems. Compared with the existing neural networks, the proposed neural network has lower model complexity and does not need penalty parameters. In the end, some numerical examples and application are given to illustrate the effectiveness and improvement of the proposed neural network. [ABSTRACT FROM AUTHOR]

The paper presents a constrained optimization procedure (COP) for the dynamic analysis of hybrid base isolation systems under earthquake excitation. After a description of the hybrid system considered, the mechanical model used for its representation is introduced, along with the governing equations. Mid-point central difference time-discretization is used to cast the computations in each time increment as a quadratic optimization problem with non-linear constraints. Numerical applications illustrate the accuracy and robustness of the formulation and highlight some typical performance characteristics of hybrid base isolation systems. [ABSTRACT FROM AUTHOR]

Seeker optimization algorithm is one of the recent swarm intelligence metaheuristics for hard optimization problems. It is based on the human group search behavior and it was successfully applied to various numerical optimization problems. While the seeker optimization algorithm was proven to be successful for different specific problems, it was not properly tested on a wide set of benchmark functions. Our testing on the standard well-known set of benchmark functions shows that the seeker optimization algorithm has serious problems with some types of functions. In this paper we introduced modifications to the seeker optimization algorithm to control exploitation/exploration balance and hybridized it with elements of the firefly algorithm that improved its exploitation capabilities. The firefly algorithm alone also exhibits deficiencies. Our proposed modified and hybridized seeker optimization algorithm not only overcame shortcomings of the original algorithms, but also outperformed other state-of-the-art swarm intelligence algorithms. [ABSTRACT FROM AUTHOR]

Real-world optimization problems have been comparatively difficult to solve due to the complex nature of the objective function with a substantial number of constraints. To deal with such problems, several metaheuristics as well as constraint handling approaches have been suggested. To validate the effectiveness and strength, performance of a newly designed approach should be benchmarked by using some complex real-world problems, instead of only the toy problems with synthetic objective functions, mostly arising from the area of numerical analysis. A list of standard real-life problems appears to be the need of the time for benchmarking new algorithms in an efficient and unbiased manner. In this study, a set of 57 real-world Constrained Optimization Problems (COPs) are described and presented as a benchmark suite to validate the COPs. These problems are shown to capture a wide range of difficulties and challenges that arise from the real life optimization scenarios. Three state-of-the-art constrained optimization methods are exhaustively tested on these problems to analyze their hardness. The experimental outcomes reveal that the selected problems are indeed challenging to these algorithms, which have been shown to solve many synthetic benchmark problems easily. [ABSTRACT FROM AUTHOR]