Mathematical Programs with Complementarity Constraints: Convergence Properties of a Smoothing Method.

Bouza, Gemayqzel; Still, Georg

In this paper, optimization problems P with complementarity constraints are considered. Characterizations for local minimizers x̄ P of Orders 1 and 2 are presented. We analyze a parametric smoothing approach for solving these programs in which P is replaced by a perturbed problem PT depending on a (small) parameter τ. We are interested in the convergence behavior of the feasible set 퓕τ and the convergence of the solutions x̄ of Pτ for τ → 0. In particular, it is shown that, under generic assumptions, the solutions x̄τ are unique and converge to a solution x̄ of P with a rate ...(√τ). Moreover, the convergence for the Hausdorff distance d(퓕τ, 퓕) between the feasible sets of Pτ and P is of order ...(√τ).

MATHEMATICAL programming; MATHEMATICAL optimization; GRAPHIC methods in statistics; HAUSDORFF measures; LINEAR complementarity problem; NONLINEAR programming

Mathematics of Operations Research, 2007, Vol 32, Issue 2, p467

1526-5471

Academic Journal

10.1287/moor.1060.0245