A Multiplier Active Set Algorithm For Mathematical Programs With Complementarity Constraints

This paper is mainly concerned for the solution to the mathematical programs withcomplementarity constraints. The main results are as following:A parameterized equivalent formulation of MPCC is obtained by using the La-grangian multiplier function, and an approach of modifying multiplier with the active-setproperty is presented. Based on this, we present a new SQP algorithm. The globalconvergence to W-stationarity of the algorithm is established under wild assumptions.Also, a new smooth multiplier sequential penalization algorithm for MPCC is pro-posed. Under the reasonable assumption and linear independence constraint qualifica-tions, it is proved that the stationary points sequence of the unconstrained penalizationproblems converges to a W-stationary point as the penalization parameter tends to infin-ity.