A Nonmonotone trust region method with adaptive radius for unconstrained optimization problems

Ahookhosh, Masoud; Amini, Keyvan

doi:10.1016/j.camwa.2010.04.034

Cited by 58 publications

(34 citation statements)

References 15 publications

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“…Two popular choices of q k are q k = −g k , which is a natural choice, and q k = −B −1 k g k , which has some interesting properties in theory and in practice, see e.g. [1,23]. In order to compare the efficiency of the new proposed adaptive radius, we use both above mentioned q k 's, but in numerical results in terms of number of iterations and function evaluations, we just focus on the case q k = −g k in order to save the computational costs in large scale problems.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…In a recent work, Cui and Wu [6] provided a nonmonotone adaptive approach based on a combination of the nonmonotone term (10) with the adaptive strategy as provided in [30]. A combination of a variant of Shi and Guo's adaptive scheme with Grippo's nonmonotone technique has been done by Ahookhosh and Amini [1]. They showed that their method is practically efficient while it has global convergence property under some standard assumptions.…”

mentioning

confidence: 96%

“…[1,15,[22][23][24]30,31], and may cause a meaningful decrease in the number of subproblem solving. Sartenaer [22] proposed a strategy for automatically determining an initial radius by letting it to be g 0 .…”

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confidence: 99%

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A relaxed nonmonotone adaptive trust region method for solving unconstrained optimization problems

Peyghami

Tarzanagh

2015

Comput Optim Appl

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In this paper, we present a new relaxed nonmonotone trust region method with adaptive radius for solving unconstrained optimization problems. The proposed method combines a relaxed nonmonotone technique with a modified version of the adaptive trust region strategy proposed by Shi and Guo (J Comput Appl Math 213:509-520, 2008). Under some suitable and standard assumptions, we establish the global convergence property as well as the superlinear convergence rate for the new method. Numerical results on some test problems show the efficiency and effectiveness of the new proposed method in practice.

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Section: Numerical Resultsmentioning

confidence: 99%

mentioning

confidence: 96%

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A relaxed nonmonotone adaptive trust region method for solving unconstrained optimization problems

Peyghami

Tarzanagh

2015

Comput Optim Appl

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“…This is one of the advantages of TR algorithms comparing with line search algorithms. TR algorithms are reliable and robust, they can be applied to ill-conditioned problems, they have very strong convergence properties, and have been proven to be theoretically and practically effective and efficient for unconstrained and equality constrained optimization problems [15][16][17]. Also, the TR algorithm has proven to be a very successful globalization technique for nonlinear programming problems with equality and inequality constraints [18,19].…”

Section: Introductionmentioning

confidence: 99%

Reference Point Based TR-PSO for Multi-Objective Environmental/Economic Dispatch

El‐Sawy¹,

Hendawy²,

El-Shorbagy³

2013

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A reference point based multi-objective optimization using a combination between trust region (TR) algorithm and particle swarm optimization (PSO) to solve the multi-objective environmental/economic dispatch (EED) problem is presented in this paper. The EED problem is handled by Reference Point Interactive Approach. One of the main advantages of the proposed approach is integrating the merits of both TR and PSO, where TR has provided the initial set (close to the Pareto set as possible and the reference point of the decision maker) followed by PSO to improve the quality of the solutions and get all the points on the Pareto frontier. The performance of the proposed algorithm is tested on standard IEEE 30-bus 6-genrator test system and is compared with conventional methods. The results demonstrate the capabilities of the proposed approach to generate true and well-distributed Pareto-optimal non-dominated solutions in one single run. The comparison with the classical methods demonstrates the superiority of the proposed approach and confirms its potential to solve the multi-objective EED problem.

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“…In addition, many adaptive nonmonotonic trust region methods have been proposed in literatures [15][16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

A Nonmonotone Weighting Self-Adaptive Trust Region Algorithm for Unconstrained Nonconvex Optimization

Lu¹,

Yang²,

Li³

et al. 2015

Discrete Dynamics in Nature and Society

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A new trust region method is presented, which combines nonmonotone line search technique, a self-adaptive update rule for the trust region radius, and the weighting technique for the ratio between the actual reduction and the predicted reduction. Under reasonable assumptions, the global convergence of the method is established for unconstrained nonconvex optimization. Numerical results show that the new method is efficient and robust for solving unconstrained optimization problems.

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A Nonmonotone trust region method with adaptive radius for unconstrained optimization problems

Cited by 58 publications

References 15 publications

A relaxed nonmonotone adaptive trust region method for solving unconstrained optimization problems

A relaxed nonmonotone adaptive trust region method for solving unconstrained optimization problems

Reference Point Based TR-PSO for Multi-Objective Environmental/Economic Dispatch

A Nonmonotone Weighting Self-Adaptive Trust Region Algorithm for Unconstrained Nonconvex Optimization

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