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First- and second-order optimality conditions for mathematical programs with vanishing constraints. (English) Zbl 1164.90407
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.

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