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author:

Peng, Zheng (Peng, Zheng.) [1] | Wu, Donghua (Wu, Donghua.) [2] | Zheng, Quan (Zheng, Quan.) [3]

Indexed by:

Scopus SCIE

Abstract:

In this paper, we propose a new method, namely the level-value estimation method, for finding global minimizer of continuous optimization problem. For this purpose, we define the variance function and the mean deviation function, both depend on a level value of the objective function to be minimized. These functions have some good properties when Newton's method is used to solve a variance equation resulting by setting the variance function to zero. We prove that the largest root of the variance equation equals the global minimal value of the corresponding optimization problem. We also propose an implementable algorithm of the level-value estimation method where importance sampling is used to calculate integrals of the variance function and the mean deviation function. The main idea of the cross-entropy method is used to update the parameters of sample distribution at each iteration. The implementable level-value estimation method has been verified to satisfy the convergent conditions of the inexact Newton method for solving a single variable nonlinear equation. Thus, convergence is guaranteed. The numerical results indicate that the proposed method is applicable and efficient in solving global optimization problems.

Keyword:

Global optimization Importance sampling Inexact Newton method Level-value estimation method Variance equation

Community:

  • [ 1 ] [Peng, Zheng]Fuzhou Univ, Coll Math & Comp Sci, Fuzhou 350108, Peoples R China
  • [ 2 ] [Wu, Donghua]Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China
  • [ 3 ] [Zheng, Quan]Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China

Reprint 's Address:

  • 彭拯

    [Peng, Zheng]Fuzhou Univ, Coll Math & Comp Sci, Fuzhou 350108, Peoples R China

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Source :

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS

ISSN: 0022-3239

Year: 2013

Issue: 2

Volume: 156

Page: 493-523

1 . 4 0 6

JCR@2013

1 . 6 0 0

JCR@2023

ESI Discipline: ENGINEERING;

JCR Journal Grade:1

CAS Journal Grade:2

Cited Count:

WoS CC Cited Count: 3

SCOPUS Cited Count: 4

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 0

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