Solving generalized semi-infinite programs by reduction to simpler problems

The article intends to give a unifying treatment of different approaches to solve generalized semi-infinite programs by transformation to simpler problems. In particular dual-, penalty-, discretization-, reduction-, and Karush-Kuhn-Tucker (KKT)-methods are applied to obtain equivalent problems or re...

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Published in:Optimization Vol. 53; no. 1; pp. 19 - 38
Main Author: Still, G.
Format: Journal Article
Language:English
Published: Taylor & Francis Group 01.02.2004
Subjects:
Discretization
Mathematics Subject Classifications 2000: 90C34
Parametric programming
Penalty methods
Semi-infinite programming with variable index sets
ISSN:0233-1934, 1029-4945
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Abstract The article intends to give a unifying treatment of different approaches to solve generalized semi-infinite programs by transformation to simpler problems. In particular dual-, penalty-, discretization-, reduction-, and Karush-Kuhn-Tucker (KKT)-methods are applied to obtain equivalent problems or relaxations of a simpler structure. The relaxations are viewed as a perturbation P τ of the original problem P, depending on a perturbation parameter τ > 0, and are analyzed by using parametric programming techniques. We give convergence results and results on the rate of convergence for the minimal values and the optimal solutions of P τ when τ tends toward 0. We review earlier studies and present new ones.
AbstractList The article intends to give a unifying treatment of different approaches to solve generalized semi-infinite programs by transformation to simpler problems. In particular dual-, penalty-, discretization-, reduction-, and Karush-Kuhn-Tucker (KKT)-methods are applied to obtain equivalent problems or relaxations of a simpler structure. The relaxations are viewed as a perturbation P τ of the original problem P, depending on a perturbation parameter τ > 0, and are analyzed by using parametric programming techniques. We give convergence results and results on the rate of convergence for the minimal values and the optimal solutions of P τ when τ tends toward 0. We review earlier studies and present new ones.
Author Still, G.
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SubjectTerms Discretization
Mathematics Subject Classifications 2000: 90C34
Parametric programming
Penalty methods
Semi-infinite programming with variable index sets
Title Solving generalized semi-infinite programs by reduction to simpler problems
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