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.