Nondifferentiable Multiplier Rules for Optimization Problems with Equilibrium Constraints

N. Movahedian; Soghra Nobakhtian

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

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.