Exact penalty results for mathematical programs with vanishing constraints. (English) Zbl 1185.90187

Summary: 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.


90C30 Nonlinear programming
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
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