First-and second-order optimality conditions for mathematical programs with vanishing constraints |
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Authors: | Tim Hoheisel Christian Kanzow |
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Institution: | (1) Institute of Mathematics, University of Würzburg, Am Hubland, 97074 Würzburg, Germany |
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Abstract: | 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.
Dedicated to Jiří V. Outrata on the occasion of his 60th birthday.
This research was partially supported by the DFG (Deutsche Forschungsgemeinschaft) under grant KA1296/15-1. |
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Keywords: | mathematical programs with vanishing constraints mathematical programs with equilibrium constraints first-order optimality conditions second-order optimality conditions |
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