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

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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.

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Authors and Affiliations

  1. Institute of Mathematics, University of Würzburg, Am Hubland, 97074, Würzburg, Germany

    Tim Hoheisel & Christian Kanzow

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  1. Tim Hoheisel
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  2. Christian Kanzow
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Correspondence to Tim Hoheisel.

Additional information

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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Hoheisel, T., Kanzow, C. First-and second-order optimality conditions for mathematical programs with vanishing constraints. Appl Math 52, 495–514 (2007). https://doi.org/10.1007/s10492-007-0029-y

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  • DOI: https://doi.org/10.1007/s10492-007-0029-y

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