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First- and second-order optimality conditions for mathematical programs with vanishing constraints
Applications of Mathematics, Tome 52 (2007) no. 6, pp. 495-514
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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.
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.
DOI : 10.1007/s10492-007-0029-y
Classification : 90C30, 90C33
Keywords: mathematical programs with vanishing constraints; mathematical programs with equilibrium constraints; first-order optimality conditions; second-order optimality conditions 
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Hoheisel, Tim; Kanzow, Christian. First- and second-order optimality conditions for mathematical programs with vanishing constraints. Applications of Mathematics, Tome 52 (2007) no. 6, pp. 495-514. doi: 10.1007/s10492-007-0029-y

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