A criterion for an approximation global optimal solution based on the filled functions

Liuyang Yuan; Zhongping Wan; Qiuhua Tang

doi:10.3934/jimo.2016.12.375

Article Contents

2016, Volume 12, Issue 1: 375-387. Doi: 10.3934/jimo.2016.12.375

This issue Previous Article Fuzzy quadratic surface support vector machine based on fisher discriminant analysis Next Article On convergence analysis of dual proximal-gradient methods with approximate gradient for a class of nonsmooth convex minimization problems

A criterion for an approximation global optimal solution based on the filled functions

1.
College of Science, Wuhan University of Science and Technology, Wuhan, Hubei, 430081
2.
School of Mathematics and Statistics, Wuhan University, Wuhan 430072
3.
Industrial Engineering Department, Wuhan University of Science and Technology, Wuhan, Hubei, 430081

Received: November 30, 2013

Revised: January 31, 2015

Published: December 2015

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Abstract

In this paper, a new definition of the filled function is given. Based on the new definition, a new class of filled functions is constructed, and the properties of the new filled functions are analysed and discussed. Moreover, according to the new class of filled functions, a criterion is given to decide whether the point we have obtained is an approximate global optimal solution. Finally, a global optimization algorithm based on the new class of filled functions is presented. The implementation of the algorithm on several test problems is reported with numerical results.

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Mathematics Subject Classification: Primary: 90C30; Secondary: 90C33.

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