Abstract

We consider a mathematical program with equilibrium constraints (MPEC). First we obtain a Lagrange multiplier rule based on the linear subdifferential involving equality, inequality and set constraints. Then we propose new constraint qualifications for M-stationary condition to hold. Finally we establish the Fritz John and Karush-Kuhn Tucker M-stationary necessary conditions for a nonsmooth (MPEC) based on the Michel-Penot subdifferential.

Author information

Contact details are reproduced from the original publication and may be historical.

N. Movahedian

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

Soghra Nobakhtian

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

nobakht@math.ui.ac.ir

Keywords

  • Optimization problems
  • necessary optimality conditions
  • constraint qualification
  • nonsmooth analysis

Mathematics Subject Classification

90C30, 90C46, 49J52

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Suggested citation

N. Movahedian, S. Nobakhtian. “Nondifferentiable Multiplier Rules for Optimization Problems with Equilibrium Constraints.” Journal of Convex Analysis 16 (2009), No. 1, 187–210. https://doi.org/10.68381/jca16010

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Published by Heldermann Verlag, 2009. Rights now held by Banach Press LLC.