Solving Mathematical Programs with Equilibrium Constraints as Constrained Equations
This paper aims at developing effective numerical methods for solving mathematical programs with equilibrium constraints. Due to the complementarity constraints, the usual constraint qualification such as the Mangasarian-Fromovitz constraint qualification does not hold at any feasible solution and there are various weaker stationary concepts such as C-/M-/S-stationarity (Clarke-/Mordukhovich-/Strong-stationarity) suggested in the literature. In this paper, we reformulate these stationary conditions as smooth equations with simple constraints. We then present a modified Levenberg-Marquardt method for solving these constrained equations. We show that, under some weak local error bound conditions, the method is locally and superlinearly convergent. Furthermore, we give some sufficient conditions for local error bounds to hold. We demonstrate by a number of examples to show that the conditions are not very stringent.
Mathematical program with equilibrium constraints C-/M-/S-stationarity constrained equation Levenberg-Marquardt method error bound superlinear convergence
Guihua Lin Lei Guo Jane J.Ye
School of Mathematical Sciences,Dalian University of Technology, Dalian, China Department of Mathematics and Statistics,University of Victoria, Victoria, Canada
国际会议
上海
英文
198-199
2010-12-10（万方平台首次上网日期，不代表论文的发表时间）