Enhanced Karush–Kuhn–Tucker Conditions for Mathematical Programs with Equilibrium Constraints

Jane J. Ye () and Jin Zhang ()
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Jane J. Ye: University of Victoria
Jin Zhang: University of Victoria

Journal of Optimization Theory and Applications, 2014, vol. 163, issue 3, No 6, 777-794

Abstract: Abstract In this paper, we study necessary optimality conditions for nonsmooth mathematical programs with equilibrium constraints. We first show that, unlike the smooth case, the mathematical program with equilibrium constraints linear independent constraint qualification is not a constraint qualification for the strong stationary condition when the objective function is nonsmooth. We then focus on the study of the enhanced version of the Mordukhovich stationary condition, which is a weaker optimality condition than the strong stationary condition. We introduce the quasi-normality and several other new constraint qualifications and show that the enhanced Mordukhovich stationary condition holds under them. Finally, we prove that quasi-normality with regularity implies the existence of a local error bound.

Keywords: Enhanced Karush–Kuhn–Tucker conditions; Constraint qualification; Mathematical program with equilibrium constraints; Local error bound (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (8)

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DOI: 10.1007/s10957-013-0493-3

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