A relaxed extragradient-like method for a class of constrained optimization problem

Biao Qu; Naihua Xiu

doi:10.3934/jimo.2007.3.645

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2007, Volume 3, Issue 4: 645-654. Doi: 10.3934/jimo.2007.3.645

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A relaxed extragradient-like method for a class of constrained optimization problem

Biao Qu^1, and
Naihua Xiu^2,

1.
Institute of Operations Research, Qufu Normal University, Shandong, 276826
2.
Department of Applied Mathematics, Beijing Jiaotong University, Beijing, 100044, P.R.

Received: September 2006

Revised: April 2007

Published: October 2007

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Abstract

This paper presents a relaxed extragradient-like method for solving the convexly constrained minimization with optimal value zero. The method is a combination of the extragradient-like algorithm and a halfspace-relaxation technique to the constrained set of the problem. Each iteration of the proposed method consists of the projection onto a halfspace containing the given closed convex set. The method is implemented very easily and is proven to be fully convergent to the solution. Preliminary computational experience is also reported.

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Mathematics Subject Classification: Primary: 90C25; Secondary: 65K05.

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