The semismooth approach for semi-infinite programming under the reduction ansatz
type: Item
instance of: scholarly article
title: The semismooth approach for semi-infinite programming under the reduction ansatz
zbMATH Open document ID: 1176.90593
author: Oliver Stein
author: Aysun Tezel
published in: Journal of Global Optimization
publication date: 2008-07-25T00:00:00Z
review text: A semismooth Newton method for solving generalized semi-infinite programming problems (GSIP) is proposed and analyzed. The method is based on the KKT system where the complementarity conditions are replaced by a formulation using NCP functions. The approach is studied for GSIP with convex lower level problems. It is shown that under standard assumptions at a local minimizer of GSIP (reduction ansatz and strict complementarity in the lower level, linear independency constraint qualification and strong second order sufficiency condition in the upper level) the standard assumptions for convergence of the semismooth Newton system holds such that the method converges q-quadratically. The approach does not assume strict comlementarity in the upper level, so that the standard KKT Newton system is singular. The paper also presents some interesting numerical examples.
Mathematics Subject Classification ID: 90C34
Mathematics Subject Classification ID: 90C33
Mathematics Subject Classification ID: 90C46
Mathematics Subject Classification ID: 49M05
Mathematics Subject Classification ID: 49M15
zbMATH DE Number: 5304070
zbMATH Keywords: generalized semi-infinite optimization
zbMATH Keywords: semismooth Newton method
zbMATH Keywords: NCP function
zbMATH Keywords: CD regularity
zbMATH Keywords: reduction ansatz
MaRDI profile type: Publication
full work available at URL: s10898-007-9228-z
OpenAlex ID: W2032951014
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DOI: 10.1007/S10898-007-9228-Z
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description: scientific article; zbMATH DE number 5304070