Hybrid approach with active set identification for mathematical programs with complementarity constraints

作者：Lin GH^*; Fukushima M

来源：Journal of Optimization Theory and Applications, 2006, 128(1): 1-28.

DOI：10.1007/s10957-005-7549-y

• mathematical programs with complementarity constraints (MPCC)
• linear independence constraint qualification (LICQ)
• B-stationarity
• M-stationarity
• C-stationarity
• asymptotically weak nondegeneracy
• identification functions

We consider a mathematical program with complementarity constraints (MPCC). Our purpose is to develop methods that enable us to compute a solution or a point with some kind of stationarity to MPCC by solving a finite number of nonlinear programs. We apply an active set identification technique to a smoothing continuation method (Ref. 1) and propose a hybrid algorithm for solving MPCC. We develop also two modifications: one makes use of an index addition strategy; the other adopts an index subtraction strategy. We show that, under reasonable assumptions, all the proposed algorithms possess a finite termination property. Further discussions and numerical experience are given as well.

• 出版日期2006-1
• 单位大连理工大学