A Dual Approach for Solving Nonlinear Infinity-Norm Minimization Problems with Applications in Separable Cases

Wajeb Gharibi 1, Yong Xia 2*

1 College of Computer Science, King Khalid University, Abha, Kingdom of Saudi Arabia
2 Institute of Computational Mathematics, The Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, P.O.~Box 2719, Beijing, 100080, China/ School of Science, Beihang University, Beijing, 100083, China

Received November 13, 2006; Accepted (in revised version) April 11, 2007
Abstract

In this paper, we consider nonlinear infinity-norm minimization problems. We device a reliable Lagrangian dual approach for solving this kind of problems and based on this method we propose an algorithm for the mixed linear and nonlinear infinity-norm minimization problems. Numerical results are presented.

Key words: Infinity-norm minimization problem; Lagrangian dual; linear program.

AMS subject classifications: 90C30

Correspondence to: Yong Xia , Institute of Computational Mathematics, The Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, P.O.~Box 2719, Beijing, 100080, China Email: yxia@lsec.cc.ac.cn