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A comparative study of sequential optimality conditions for mathematical programs with cardinality constraints. (English) Zbl 1487.90608

Summary: We propose a comparative study of sequential optimality conditions for mathematical programs with cardinality constraints. Besides analyzing some of the classical approximate conditions for nonlinear programming, such as AKKT, CAKKT and PAKKT, we also propose an approximate weak stationarity (AW-stationarity) concept designed to deal with this class of problems and we prove that it is a legitimate optimality condition independently of any constraint qualification. We point out that, despite the computational appeal of the sequential optimality conditions, in this work we are not concerned with algorithmic consequences. Our aim is purely to discuss theoretical aspects of such conditions for MPCaC problems.

MSC:

90C30 Nonlinear programming
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
90C46 Optimality conditions and duality in mathematical programming

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