A wedge trust region method with self-correcting geometry for  derivative-free optimization

Liang  Zhang; Wenyu  Sun; Raimundo  J. B. de  Sampaio; Jinyun  Yuan

doi:10.3934/naco.2015.5.169

Article Contents

2015, Volume 5, Issue 2: 169-184. Doi: 10.3934/naco.2015.5.169

This issue Previous Article Speeding up a memetic algorithm for the max-bisection problem Next Article A new semidefinite relaxation for $L_{1}$-constrained quadratic optimization and extensions

A wedge trust region method with self-correcting geometry for derivative-free optimization

1.
School of Mathematical Sciences, Jiangsu Key Labratory for NSLSCS, Nanjing Normal University, Nanjing 210023
2.
PPGEPS, Pontifical Catholic University of Parana (PUCPR), Curitiba, Parana
3.
Department of Mathematics, Universidade Federal do Parana (UFPR), Curitiba, Parana

Received: November 30, 2014

Revised: March 31, 2015

Published: May 2015

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Abstract

Recently, some methods for solving optimization problems without derivatives have been proposed. The main part of these methods is to form a suitable model function that can be minimized for obtaining a new iterative point. An important strategy is geometry-improving iteration for a good model, which needs a lot of calculations. Besides, Marazzi and Nocedal (2002) proposed a wedge trust region method for derivative free optimization. In this paper, we propose a new self-correcting geometry procedure with less computational efforts, and combine it with the wedge trust region method. The global convergence of new algorithm is established. The limited numerical experiments show that the new algorithm is efficient and competitive.

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Mathematics Subject Classification: Primary: 65K05; Secondary: 90C30.

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References

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