A modified nonmonotone trust region line search method

Rezaee, Saeed; Babaie-Kafaki, Saman

doi:10.1007/s12190-017-1113-4

Cited by 6 publications

(4 citation statements)

References 17 publications

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“…The problem has widely used in many applications based on medical science, optimal control, and functional approximation, etc. As we all know, there are many methods for solving unconstrained optimization problems, such as the conjugate gradient method [1][2][3], the Newton method [4,5], and the trust region method [6][7][8]. Constrained optimization problems can also be solved by processing constraint conditions and transforming them into unconstrained optimization problems.…”

Section: Introductionmentioning

confidence: 99%

“…Based on this situation, Nocedal and Yuan [9] proposed an algorithm in 1998, combining the trust region method and the line search method for the first time. Inspired by this, Michael et al, Li et al, and Zhang et al proposed a trust region method with the line search strategy ([10-12], respectively).As can be seen in other works [4,7,8] monotone techniques are distinguished from nonmonotone techniques in that the value of the function needs to be reduced at each iteration; at the same time, the use of nonmonotone techniques can not only guarantee finding the global optimal solution effectively, but also improve the convergence rate of the algorithm. The watchdog technique was presented by Chamberlain et al [13] in 1982 to overcome the Maratos effect of constrained optimization problems.…”

mentioning

confidence: 97%

“…As can be seen in other works [4,7,8] monotone techniques are distinguished from nonmonotone techniques in that the value of the function needs to be reduced at each iteration; at the same time, the use of nonmonotone techniques can not only guarantee finding the global optimal solution effectively, but also improve the convergence rate of the algorithm. The watchdog technique was presented by Chamberlain et al [13] in 1982 to overcome the Maratos effect of constrained optimization problems.…”

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confidence: 99%

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A Filter and Nonmonotone Adaptive Trust Region Line Search Method for Unconstrained Optimization

Ding

Wang

2020

Symmetry

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In this paper, a new nonmonotone adaptive trust region algorithm is proposed for unconstrained optimization by combining a multidimensional filter and the Goldstein-type line search technique. A modified trust region ratio is presented which results in more reasonable consistency between the accurate model and the approximate model. When a trial step is rejected, we use a multidimensional filter to increase the likelihood that the trial step is accepted. If the trial step is still not successful with the filter, a nonmonotone Goldstein-type line search is used in the direction of the rejected trial step. The approximation of the Hessian matrix is updated by the modified Quasi-Newton formula (CBFGS). Under appropriate conditions, the proposed algorithm is globally convergent and superlinearly convergent. The new algorithm shows better performance in terms of the Dolan-Moré performance profile. Numerical results demonstrate the efficiency and robustness of the proposed algorithm for solving unconstrained optimization problems. Symmetry 2020, 12, 656 2 of 22where . is the Euclidean norm, f k = f (x k ), g k = ∇ f (x k ), B k is a symmetric approximation matrix of G k = ∇ 2 f (x k ), and ∆ k is a trust region radius.Traditional trust region methods have some disadvantages, such as the fact that the subproblem needs to be solved many times to obtain an acceptable trial step within one iteration, which leads to high computational costs for the iterative process. One way to overcome this disadvantage is to use a line search strategy in the direction of the rejected trial step. Based on this situation, Nocedal and Yuan [9] proposed an algorithm in 1998, combining the trust region method and the line search method for the first time. Inspired by this, Michael et al., Li et al., and Zhang et al. proposed a trust region method with the line search strategy ([10-12], respectively).As can be seen in other works [4,7,8] monotone techniques are distinguished from nonmonotone techniques in that the value of the function needs to be reduced at each iteration; at the same time, the use of nonmonotone techniques can not only guarantee finding the global optimal solution effectively, but also improve the convergence rate of the algorithm. The watchdog technique was presented by Chamberlain et al. [13] in 1982 to overcome the Maratos effect of constrained optimization problems. Motivated by this idea, a nonmonotone line search technique was proposed by Grippo et al. [14] in 1986. The step length α k satisfies the following inequality:

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Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 97%

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confidence: 99%

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A Filter and Nonmonotone Adaptive Trust Region Line Search Method for Unconstrained Optimization

Ding

Wang

2020

Symmetry

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“…The literature contains justifiable studies on the radii and the ratios of the TR methods; (see, e.g. Rezaee and Babaie-Kafaki, 2018;Rezaee and Babaie-Kafaki, 2019;Yuan, 2015 and the references therein).…”

Section: Introductionmentioning

confidence: 99%

A randomized nonmonotone adaptive trust region method based on the simulated annealing strategy for unconstrained optimization

Babaie-Kafaki

Rezaee

2019

IJICC

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Purpose The purpose of this paper is to employ stochastic techniques to increase efficiency of the classical algorithms for solving nonlinear optimization problems. Design/methodology/approach The well-known simulated annealing strategy is employed to search successive neighborhoods of the classical trust region (TR) algorithm. Findings An adaptive formula for computing the TR radius is suggested based on an eigenvalue analysis conducted on the memoryless Broyden-Fletcher-Goldfarb-Shanno updating formula. Also, a (heuristic) randomized adaptive TR algorithm is developed for solving unconstrained optimization problems. Results of computational experiments on a set of CUTEr test problems show that the proposed randomization scheme can enhance efficiency of the TR methods. Practical implications The algorithm can be effectively used for solving the optimization problems which appear in engineering, economics, management, industry and other areas. Originality/value The proposed randomization scheme improves computational costs of the classical TR algorithm. Especially, the suggested algorithm avoids resolving the TR subproblems for many times.

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Fault Location Method for Two-Terminal Untransposed Overhead Lines in Distribution Networks Measured by μMPMU

2021

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With the rapid development of distribution networks, two-terminal overhead lines have been used on a large scale for higher power supply reliability, thus the fault location has attracted much attention. Accurate fault location is helpful to shorten the outage time and improve the economy of operation greatly. However, since insufficient standardization of equipment selection and poor management, line parameters are usually inaccurate or even unknown, mature fault location methods based on impedance can’t be applied anymore. Also, the asymmetry caused by non-transposition in distribution networks affects the accuracy of fault location. This paper proposes a fault location method for two-terminal untransposed overhead lines without requiring line parameters. Firstly, this paper considers parameter asymmetry, and the mutual impedances between the three phases are set as different values. Secondly, the location equations rely on three-phase networks, then the self-impedance and mutual impedances are regarded as unknowns and solved directly. Finally, this method takes the average value of fundamental frequency components from different data windows, which reduces error and improves accuracy. The simulation results show that the fault location method has high accuracy, and can effectively overcome the influence of unknown line parameters and non-transposition.

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A modified nonmonotone trust region line search method

Cited by 6 publications

References 17 publications

A Filter and Nonmonotone Adaptive Trust Region Line Search Method for Unconstrained Optimization

A Filter and Nonmonotone Adaptive Trust Region Line Search Method for Unconstrained Optimization

A randomized nonmonotone adaptive trust region method based on the simulated annealing strategy for unconstrained optimization

Fault Location Method for Two-Terminal Untransposed Overhead Lines in Distribution Networks Measured by μMPMU

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