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

Hoheisel, Tim; Kanzow, Christian

Appl. Math., Praha 52, No. 6, 495-514 (2007).

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.

MSC:

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

Keywords:

mathematical programs with vanishing constraints; mathematical programs with equilibrium constraints; first-order optimality conditions; second-order optimality conditions

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