New Constraint Qualifications for S-Stationarity for MPEC with Nonsmooth Objective

Peng Zhang (), Jin Zhang (), Gui-Hua Lin and Xinmin Yang ()
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Peng Zhang: School of Management, Shanghai University, Shanghai 200444, P. R. China
Jin Zhang: Department of Mathematics, Southern University of Science and Technology, Shenzhen, P. R. China
Gui-Hua Lin: School of Management, Shanghai University, Shanghai 200444, P. R. China
Xinmin Yang: College of Mathematics Science, Chongqing Normal University, Chongqing 401131, P. R. China

Asia-Pacific Journal of Operational Research (APJOR), 2019, vol. 36, issue 02, 1-16

Abstract: This paper considers a mathematical problem with equilibrium constraints (MPEC) in which the objective is locally Lipschitz continuous but not continuously differentiable everywhere. Our focus is on constraint qualifications for the nonsmooth S-stationarity in the sense of the limiting subdifferentials. First, although the MPEC-LICQ is not a constraint qualification for the nonsmooth S-stationarity, we show that the MPEC-LICQ can serve as a constraint qualification for the nonsmooth S-stationarity under some kind of regularity. Then, we extend some new constraint qualifications for nonlinear programs to the considered nonsmooth MPEC and show that all of them can serve as constraint qualifications for the nonsmooth S-stationarity. We further extend these results to the multiobjective case.

Keywords: MPEC; nonsmoothness; constraint qualification; S-stationarity (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1142/S0217595919400013

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