First-and second-order optimality conditions for mathematical programs with vanishing constraints

We consider a special class of optimization problems that we call Mathematical Programs with Vanishing Constraints, MPVC for short, which serves as a unified framework for several applications in structural and topology optimization. Since an MPVC most often violates stronger standard constraint qua...

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Bibliographic Details
Published in:Applications of mathematics (Prague) 2007-12, Vol.52 (6), p.495-514
Main Authors: Hoheisel, Tim, Kanzow, Christian
Format: Article
Language:English
Subjects:
Optimization
Studies
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Summary:We consider a special class of optimization problems that we call Mathematical Programs with Vanishing Constraints, MPVC for short, which serves as a unified framework for several applications in structural and topology optimization. Since an MPVC most often violates stronger standard constraint qualification, first-order necessary optimality conditions, weaker than the standard KKT-conditions, were recently investigated in depth. This paper enlarges the set of optimality criteria by stating first-order sufficient and second-order necessary and sufficient optimality conditions for MPVCs.[PUBLICATION ABSTRACT]
ISSN:0862-7940
1572-9109
DOI:10.1007/s10492-007-0029-y