Operations Research Transactions ›› 2014, Vol. 18 ›› Issue (4): 119-130.

• Original Articles • Previous Articles    

 A multiplier relaxation method for solving mathematical programs with complementarity constraints

LIU Shuixia1,*, CHEN Guoqing1   

  1. 1. School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China
  • Received:2014-04-18 Online:2014-12-15 Published:2014-12-15

Abstract: By using the Lagrange function of the complementarity problem, a new relaxed problem of MPCC is given. We show that the linear independence constraint qualification holds for the new relaxed problem under some mild conditions. Based on this, a multiplier relaxed method for solving MPCC is presented. The limited point of stationary points of the relaxed problems is M-stationary point under the MPCC-LICQ. Without requiring the second-order necessary condition, the limited point is B-stationary point if the ULSC holds. At last, we propose a new condition for convergence to B-stationary point.

Key words: mathematical programs with complementarity constraints, Lagrange function, upper lever strict complementarity, B-stationary point

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