A three-dimension null-space approach for mathematical programs with equilibrium constraints

Abstract

Recently, some traditional optimization methods are employed to mathematical programs with equilibrium constraints (MPECs), for example, Fletcher et al. using SQP methods. Researchers aim to transform a MPEC into a traditional nonlinear programming. Now, we focus on the form of MPECs and a new method is brought forward. In this work, a three-dimension null-space method is put forward and is applied in a MPECs. In a traditional null-space method, a step is consisted of two components, vertical part and range part. But to solve MPECs, a step is composed of three parts, which are related to nonlinear inequality constraints, the complementarity conditions and the objective function. Therefore, a new method for MPECs is proposed and null-space method is extend not only in form but also for problems. Furthermore, it is the beginning to propose three-dimensions methods, which is interesting in theory and in practice.