Article ID: | iaor20111363 |
Volume: | 30 |
Issue: | 2 |
Start Page Number: | 169 |
End Page Number: | 194 |
Publication Date: | Nov 2004 |
Journal: | Journal of Global Optimization |
Authors: | Qi Liqun, Wu Soon-Yi, Li Dong-Hui, Tam Judy |
Keywords: | Newton method, Programming (semi-infinite) |
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.