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Paper   IPM / M / 13795
School of Mathematics
  Title:   Optimality conditions for nonsmooth mathematical programs with equilibrium constraints, using convexificators
  Author(s):  S. Nobakhtian (Joint with A. Ansari Ardali and N. Movahedian)
  Status:   Published
  Journal: Optimization
  Vol.:  65
  Year:  2016
  Pages:   67-85
  Supported by:  IPM
In this paper, we deal with constraint qualifications, stationary concepts and optimality conditions for a nonsmooth mathematical program with equilibrium constraints (MPEC). The main tool in our study is the notion of convexificator. Using this notion, standard and MPEC Abadie and several other constraint qualifications are proposed and a comparison between them is presented. We also define nonsmooth stationary conditions based on the convexificators. In particular,we show that GS-stationary is the first-order optimality condition under generalized standard Abadie constraint qualification. Finally, sufficient conditions for global or local optimality are derived under some MPECgeneralized convexity assumptions.

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