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October  2007, 3(4): 645-654. doi: 10.3934/jimo.2007.3.645

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, China
2. 

Department of Applied Mathematics, Beijing Jiaotong University, Beijing, 100044, P.R., China

Received  September 2006 Revised  April 2007 Published  October 2007

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.
Keywords: convex optimization, Relaxed extragradient-like method, halfspace-relaxation technique, fully convergent..
Mathematics Subject Classification: Primary: 90C25; Secondary: 65K0.
Citation: Biao Qu, Naihua Xiu. A relaxed extragradient-like method for a class of constrained optimization problem. Journal of Industrial & Management Optimization, 2007, 3 (4) : 645-654. doi: 10.3934/jimo.2007.3.645
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