ONE-PARAMETRIC SCHEMES FOR SOLVING MATHEMATICAL PROGRAMS WITH COMPLEMENTARITY CONSTRAINTS: THEORETICAL PROPERTIES

Abstract

Due to the complex disjunctive structure of mathematical programs with complementarity con- straints (MPCC), parametric approaches are used to overcome this difficulty. The underlying idea is to solve a program depending on the real parameter τ ≥ 0, where τ = 0 corresponds to the original MPCC program. The paper considers seven approaches: two based on smoothing the complemen- tarity constraints and the other five, on their regularisation. We consider the point-to-set functions that, for each value of the parameter τ , define the set of feasible solutions and the set of optimal solution of the parametric problems they define. We study the distance between the feasible sets and the set of minimisers of the parametric program for τ going to zero.