Semismooth Newton Methods for Solving Semi-Infinite Programming Problems

Authors:
Liqun Qi;Soon-Yi Wu;Guanglu Zhou
Affiliations:
Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong (e-mail: maqilq@polyu.edu.hk)/;Institute of Applied Mathematics, National Cheng-Kung University, Tainan 700, Taiwan (e-mail: soonyi@mail.ncku.edu.tw)/;Department of Mathematics, National University of Singapore, Singapore (e-mail: smazgl@nus.edu.sg).
Venue:
Journal of Global Optimization
Year:
2003

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Abstract

In this paper we present some semismooth Newton methods for solving the semi-infinite programming problem. We first reformulate the equations and nonlinear complementarity conditions derived from the problem into a system of semismooth equations by using NCP functions. Under some conditions a solution of the system of semismooth equations is a solution of the problem. Then some semismooth Newton methods are proposed for solving this system of semismooth equations. These methods are globally and superlinearly convergent. Numerical results are also given.