A Smoothing Newton Method for Semi‐Infinite Programming

A Smoothing Newton Method for Semi‐Infinite Programming

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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: , , ,
Keywords: Newton method, Programming (semi-infinite)
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.

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