Exact penalty results for mathematical programs with vanishing constraints |
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Authors: | Tim Hoheisel Ji?í V Outrata |
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Institution: | a University of Würzburg, Institute of Mathematics, Am Hubland, 97074 Würzburg, Germany b Academy of Sciences, Institute of Information Theory and Automation, 18208 Prague, Czech Republic |
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Abstract: | A mathematical program with vanishing constraints (MPVC) is a constrained optimization problem arising in certain engineering applications. The feasible set has a complicated structure so that the most familiar constraint qualifications are usually violated. This, in turn, implies that standard penalty functions are typically non-exact for MPVCs. We therefore develop a new MPVC-tailored penalty function which is shown to be exact under reasonable assumptions. This new penalty function can then be used to derive (or recover) suitable optimality conditions for MPVCs. |
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Keywords: | Mathematical programs with vanishing constraints Mathematical programs with equilibrium constraints Exact penalization Calmness Subdifferential calculus Limiting normal cone |
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