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This paper presents a new numerical method to solve the non-linear constitutive equations of viscoelastic string with variable fractional order model. Firstly, the non-linear constitutive equation of the string is established based on the variable fractional viscoelastic model. Secondly, non-linear constitutive equation of the string is transformed into a matrix equation by using Bernstein polynomials, which can greatly simplify the solving process. Then the matrix equation is discretized and solved to obtain the numerical solutions. Finally, numerical results of viscoelastic string show the effect of the axial tension and axial velocity on its displacement, velocity and acceleration. It also indicates that how dynamic behaviours are affected by external force excitation. In addition, the proposed algorithm shows enormous potentials for solving the problem of high precision dynamics with the variable fractional order model. [ABSTRACT FROM AUTHOR]

The paper proposes a new extragradient algorithm for solving strongly pseudomonotone equilibrium problems which satisfy a Lipschitz-type condition recently introduced by Mastroeni in auxiliary problem principle. The main novelty of the paper is that the algorithm generates the strongly convergent sequences in Hilbert spaces without the prior knowledge of Lipschitz-type constants and any hybrid method. Several numerical experiments on a test problem are also presented to illustrate the convergence of the algorithm. [ABSTRACT FROM AUTHOR]

In this paper, based on a new smoothing function, the general box constrained variational inequalities are solved by a smoothing Newton algorithm with a nonmonotone line search. The proposed algorithm is proved to be globally and locally superlinearly convergent under suitable assumptions. The preliminary numerical results are reported. [ABSTRACT FROM AUTHOR]

In this paper, existence of critical point and weak efficient point of vector optimization problem is studied. A sequence of points in n-dimension is generated using positive definite matrices like Quasi-Newton method. It is proved that accumulation points of this sequence are critical points or weak efficient points under different conditions. An algorithm is provided in this context. This method is free from any kind of priori chosen weighting factors or any other form of a priori ranking or ordering information for objective functions. Also, this method does not depend upon initial point. The algorithm is verified in numerical examples. [ABSTRACT FROM AUTHOR]

The Bregman function-based Proximal Point Algorithm (BPPA) is an efficient tool for solving equilibrium problems and fixed-point problems. Extending rather classical proximal regularization methods, the main additional feature consists in an application of zone coercive regularizations. The latter allows to treat the generated subproblems as unconstrained ones, albeit with a certain precaution in numerical experiments. However, compared to the (classical) Proximal Point Algorithm for equilibrium problems, convergence results require additional assumptions which may be seen as the price to pay for unconstrained subproblems. Unfortunately, they are quite demanding – for instance, as they imply a sort of unique solvability of the given problem. The main purpose of this paper is to develop a modification of the BPPA, involving an additional extragradient step with adaptive (and explicitly given) stepsize. We prove that this extragradient step allows to leave out any of the additional assumptions mentioned above. Hence, though still of interior proximal type, the suggested method is applicable to an essentially larger class of equilibrium problems, especially including non-uniquely solvable ones. [ABSTRACT FROM AUTHOR]

In this paper, a numerical algorithm is proposed based on the method of fundamental solutions (MFS) for the Cauchy problem connected with the Laplace equation in ℝ2. The major advantage of the modified MFS is to keep a very basic natural property, i.e. the invariance under trivial coordinate changes in the problem description. The method combines Newton's method and classic Tikhonov regularization to solve an inverse problem. The numerical convergence, accuracy, and stability of the method with respect to increasing the number of source points, and decreasing the amount of noise added into the input data, respectively, are also analysed with some examples, even for high noise levels. [ABSTRACT FROM PUBLISHER]

The glmnet package by Friedmanet al.[Regularization paths for generalized linear models via coordinate descent, J. Statist. Softw. 33 (2010), pp. 1–22] is an extremely fast implementation of the standard coordinate descent algorithm for solving ℓ1penalized learning problems. In this paper, we consider a family of coordinate majorization descent algorithms for solving the ℓ1penalized learning problems by replacing each coordinate descent step with a coordinate-wise majorization descent operation. Numerical experiments show that this simple modification can lead to substantial improvement in speed when the predictors have moderate or high correlations. [ABSTRACT FROM PUBLISHER]

This paper first proposes a trust region algorithm to obtain a stationary point of unconstrained multiobjective optimisation problem. Under suitable assumptions, the global convergence of the new algorithm is established. We then extend the trust region method to solve the non-smooth multiobjective optimisation problem. [ABSTRACT FROM PUBLISHER]

In this paper, we propose nonlinear programming (NLP) formulations and difference of convex functions (DC) programming approaches for the asymmetric eigenvalue complementarity problem (EiCP). The EiCP has a solution if and only if these NLP formulations have zero global optimal value. We reformulate the NLP formulations as DC programs which can be efficiently solved by a DC algorithm. Some preliminary numerical results illustrate the good performance of the proposed methods. [ABSTRACT FROM PUBLISHER]

This paper presents a new trust-region procedure for solving symmetric nonlinear systems of equations having several variables. The proposed approach takes advantage of the combination of both an effective adaptive trust-region radius and a non-monotone strategy. It is believed that the selection of an appropriate adaptive radius and the application of a suitable non-monotone strategy can improve the efficiency and robustness of the trust-region framework as well as decrease the computational costs of the algorithm by decreasing the required number of subproblems to be solved. The global convergence and the quadratic convergence of the proposed approach are proved without the non-degeneracy assumption of the exact Jacobian. The preliminary numerical results of the proposed algorithm indicating the promising behaviour of the new procedure for solving nonlinear systems are also reported. [ABSTRACT FROM PUBLISHER]

Augmented Lagrangian methods are effective tools for solving large-scale nonlinear programming problems. At each outer iteration, a minimization subproblem with simple constraints, whose objective function depends on updated Lagrange multipliers and penalty parameters, is approximately solved. When the penalty parameter becomes very large, solving the subproblem becomes difficult; therefore, the effectiveness of this approach is associated with the boundedness of the penalty parameters. In this paper, it is proved that under more natural assumptions than the ones employed until now, penalty parameters are bounded. For proving the new boundedness result, the original algorithm has been slightly modified. Numerical consequences of the modifications are discussed and computational experiments are presented. [ABSTRACT FROM AUTHOR]

Particle swarm optimization (PSO) is a population-based stochastic and derivative-free method that has been used to solve various optimization problems due to its simplicity and efficiency. While solving high-dimensional or complicated problems, PSO requires a large number of particles to explore the problem domains and consequently introduces high computational costs. In this paper, we focus on the acceleration of PSO for solving box-constrained, load-balanced optimization problems by parallelization on a graphics processing unit (GPU). We propose a GPU-accelerated PSO (GPSO) algorithm by using a thread pool model and implement GPSO on a GPU. Numerical results show that the GPU architecture fits the PSO framework well by reducing computational timing, achieving high parallel efficiency and finding better optimal solutions by using a large number of particles. For example, while solving the 100-dimensional test problems with 65,536 (16×212) particles, GPSO has achieved up to 280X and 83X speedups on a NVIDIA Tesla C1060 1.30 GHz GPU relative to an Intel Xeon-X5450 3.00 GHz central processing unit running in single- and quad-core mode, respectively. GPSO provides a promising method for tackling high-dimensional and difficult optimization problems using a low-cost and many-core GPU system. [ABSTRACT FROM PUBLISHER]

Detection of copositivity plays an important role in combinatorial and quadratic optimization. Recently, an algorithm for copositivity detection by simplicial partition has been proposed. In this paper, we develop an improved depth-first simplicial partition algorithm which reduces memory requirements significantly and therefore enables copositivity checks of much larger matrices - of size up to a few thousands instead of a few hundreds. The algorithm has been investigated experimentally on a number of MaxClique problems as well as on generated random problems. We present numerical results showing that the algorithm is much faster than a recently published linear algebraic algorithm for copositivity detection based on traditional ideas - checking properties of principal sub-matrices. We also show that the algorithm works very well for solving MaxClique problems through copositivity checks. [ABSTRACT FROM AUTHOR]

The paper describes the design of our interior-point implementation to solve large-scale quadratically constrained convex optimization problems. We outline the details of the implemented algorithm, which is based on the primal-dual interior-point method. Our discussion includes topics related to starting point strategies and to the implementation of the numerical algebra employed, with emphasis on sparsity and stability issues. Computational results are given on a demonstrative set of convex quadratically constrained quadratic problems. [ABSTRACT FROM AUTHOR]

In this paper, an algorithm is introduced for feasibility problems associated with frequency-dependent, linear matrix inequalities - these problems correspond to H2 or H∞ robust performance tests for a given controller, in the face of feedback perturbations. To this effect, an auxiliary H2 cost-functional is introduced and a sequence of H2 problems with a single linear constraint is considered in which the H2 cost-functional is kept unchanged while the linear constraints are iteratively modified. It is shown that, in each step, the auxiliary optimal solution moves closer (in the sense of a weighted quadratic norm) to the target feasible set. Conditions are also established under which the sequence of solutions to the auxiliary problems yields a solution to the original feasibility problem. The method is illustrated by a numerical example corresponding to a H∞ robust performance test for a multivariable system. [ABSTRACT FROM AUTHOR]