Department of Applied Mathematics & Physics, Kyoto Univiversity

Technical Report #99005 (March, 1999)

Convergence of a Smoothing Continuation Method for Mathematical Programs with Complementarity Constraints
by Masao Fukushima and Jong-Shi Pang

We study the behavior of a sequence generated by a smoothing continuation method for mathematical programs with equilibrium constraints (MPEC). In particular, we show that under the linear independence constraint qualification and an additional condition called the asymptotic weak nondegeneracy, the limit of KKT points satisfying the second-order necessary conditions for the perturbed problems is a B-stationary point of the original MPEC. The notable fact is that this result does not rely on the strict complementarity assumption at the limit point.