A nonmonotone trust-region line search method for large-scale unconstrained optimization

Ahookhosh, Masoud; Amini, Keyvan; Peyghami, M. Reza

doi:10.1016/j.apm.2011.07.021

Cited by 65 publications

(53 citation statements)

References 13 publications

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“…Else, compute r N R k and r NC k by (8) and (11), respectively. Update ν k using (13), and set Δ k = min{Δ k , Δ max }, whereΔ k is given by (12).…”

Section: Algorithm 31 [A New Nonmonotone Adaptive Retrospective Tr Mmentioning

confidence: 99%

“…Despite many advantages of their technique, it suffers from some drawbacks; see, e.g., [11,12]. In order to overcome these shortcomings, several nonmonotone terms have been introduced in the literature; see, e.g., [11][12][13][14]. A brief look at the results reveals that the nonmonotone term proposed in [12,13] is more efficient than those in [10,11,14].…”

Section: Introductionmentioning

confidence: 99%

“…In order to overcome these shortcomings, several nonmonotone terms have been introduced in the literature; see, e.g., [11][12][13][14]. A brief look at the results reveals that the nonmonotone term proposed in [12,13] is more efficient than those in [10,11,14]. Recently, Chen et al [15] suggested a nonmonotone TR method in which the retrospective ratio [2] is appropriately modified for updating the radii.…”

Section: Introductionmentioning

confidence: 99%

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A New Nonmonotone Adaptive Retrospective Trust Region Method for Unconstrained Optimization Problems

Tarzanagh

Peyghami

Bastin

2015

J Optim Theory Appl

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In this paper, we propose a new nonmonotone adaptive retrospective Trust Region (TR) method for solving unconstrained optimization problems. Inspired by the retrospective ratio proposed in Bastin et al. (Math Program Ser A 123:395-418, 2010), a new nonmonotone TR ratio is introduced based on a convex combination of the nonmonotone classical and retrospective ratios. Due to the value of the new ratio, the TR radius is updated adaptively by a variant of the rule as proposed in Shi and Guo (J Comput Appl Math 213:509-520, 2008). Global convergence property of the new algorithm, as well as its superlinear convergence rate, is established under some standard assumptions. Numerical results on some test problems show the efficiency and effectiveness of the new method in practice, too.

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“…Else, compute r N R k and r NC k by (8) and (11), respectively. Update ν k using (13), and set Δ k = min{Δ k , Δ max }, whereΔ k is given by (12).…”

Section: Algorithm 31 [A New Nonmonotone Adaptive Retrospective Tr Mmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A New Nonmonotone Adaptive Retrospective Trust Region Method for Unconstrained Optimization Problems

Tarzanagh

Peyghami

Bastin

2015

J Optim Theory Appl

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“…Otherwise, the TR radius must be diminished and the sub-problem (3) must be solved again [14]. Figure 1 shows the mechanism of TR algorithm.…”

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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“…Therefore, it is necessary to design a time-saving algorithms. Trust-region method of quadratic model for unconstrained optimization has been studied by many researchers [14][15][16][17]. Trust-region methods are robust, can be applied to ill-conditioned problems and have strong global convergence properties.…”

Section: Introductionmentioning

confidence: 99%

A Multi-Beam Model of Antenna Array Pattern Synthesis Based on Conic Trust Region Method

Feng¹

2013

PIER B

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Abstract-In this paper, we propose a multi-beam model for antenna array pattern synthesis (AAPS) problem. The model uses a conic trust region algorithm (CTRA) similarly proposed in this paper to optimize its cost function. Undoubtedly, whole algorithm efficiency ultimately lies on the CTRA, thereof, we propose a method to improve the iterative algorithm's efficiency. Unlike traditional trust region methods that resolve sub-problems, the CTRA efficiently searches a region via solving a inequation, by which it identifies new iteration points when a trial step is rejected. Thus, the proposed algorithm improves computational efficiency. Moreover, the CTRA has strong convergence properties with the local superlinear and quadratic convergence rate under mild conditions, and exhibits high efficiency and robustness. Finally, we apply the combinative algorithm to AAPS. Numerical results show that the method is highly robust, and computer simulations indicate that the algorithm excellently performs AAPS problem.

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A nonmonotone trust-region line search method for large-scale unconstrained optimization

Cited by 65 publications

References 13 publications

A New Nonmonotone Adaptive Retrospective Trust Region Method for Unconstrained Optimization Problems

A New Nonmonotone Adaptive Retrospective Trust Region Method for Unconstrained Optimization Problems

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

A Multi-Beam Model of Antenna Array Pattern Synthesis Based on Conic Trust Region Method

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