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Scaled constraint qualifications for generalized equation constrained problems and application to nonsmooth mathematical programs with equilibrium constraints

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Abstract

In this paper, the notion of graphical derivatives is applied to define a new class of several well-known constraint qualifications for a nonconvex multifunction M at a point of its graph. This class is called as “scaled constraint qualifications”. The reason of this terminology is that these conditions ensure the existence of bounded KKT multiplier vectors with a proper upper bound. The relations between these constraint qualifications and stability properties of M are also investigated. New sharp necessary optimality conditions with bounded multiplier vectors are derived for an optimization problem with a generalized equation constraint. The results are adapted to nonsmooth general constrained problems and nonsmooth mathematical programs with equilibrium constraints.

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  1. Department of Mathematics, University of Isfahan, P. O. Box 81745-163, Isfahan, Iran

    Nooshin Movahedian

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  1. Nooshin Movahedian
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Movahedian, N. Scaled constraint qualifications for generalized equation constrained problems and application to nonsmooth mathematical programs with equilibrium constraints. Positivity 24, 253–285 (2020). https://doi.org/10.1007/s11117-019-00676-2

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