A Smoothing Newton Method for Semi-Infinite Programming

Authors:
Dong-Hui Li;Liqun Qi;Judy Tam;Soon-Yi Wu
Affiliations:
Department of Applied Mathematics, Hunan University Changsha, China;Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong;Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong;Department of Applied Mathematics, Hunan University Changsha, China
Venue:
Journal of Global Optimization
Year:
2004

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Abstract

This paper is concerned with numerical methods for solving a semi-infinite programming problem. We reformulate the equations and nonlinear complementarity conditions of the first order optimality condition of the problem into a system of semismooth equations. By using a perturbed Fischer--Burmeister function, we develop a smoothing Newton method for solving this system of semismooth equations. An advantage of the proposed method is that at each iteration, only a system of linear equations is solved. We prove that under standard assumptions, the iterate sequence generated by the smoothing Newton method converges superlinearly/quadratically.