Generalized stationary points and an interior-point method for mathematical programs with equilibrium constraints

被引：0
作者：
Xinwei Liu
Jie Sun
机构：
[1] National University of Singapore and Department of Applied Mathematics,Singapore
[2] National University of Singapore,MIT Alliance
来源：
Mathematical Programming | 2004年 / 101卷
关键词：
Global convergence; Interior-point methods; Mathematical programming with equilibrium constraints; Stationary point;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Generalized stationary points of the mathematical program with equilibrium constraints (MPEC) are studied to better describe the limit points produced by interior point methods for MPEC. A primal-dual interior-point method is then proposed, which solves a sequence of relaxed barrier problems derived from MPEC. Global convergence results are deduced under fairly general conditions other than strict complementarity or the linear independence constraint qualification for MPEC (MPEC-LICQ). It is shown that every limit point of the generated sequence is a strong stationary point of MPEC if the penalty parameter of the merit function is bounded. Otherwise, a point with certain stationarity can be obtained. Preliminary numerical results are reported, which include a case analyzed by Leyffer for which the penalty interior-point algorithm failed to find a stationary point.
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页码：231 / 261
页数：30
相关论文
共 26 条
  • [1] Aiyoshi undefined(1981)undefined IEEE Trans. Syst., Man, Cybern., SMC 11 444-undefined
  • [2] Bard undefined(1988)undefined Math. Program. 40 15-undefined
  • [3] Ben-Ayed undefined(1990)undefined Oper. Res. 38 556-undefined
  • [4] Byrd undefined(1999)undefined SIAM J. Optim. 9 877-undefined
  • [5] Chen undefined(1995)undefined Optim. 32 193-undefined
  • [6] Clark undefined(1988)undefined Naval Research Logistics Quarterly 35 413-undefined
  • [7] Dolan undefined(2002)undefined Math. Program., Ser. A 91 201-undefined
  • [8] Facchinei undefined(1999)undefined Math. Program. 85 107-undefined
  • [9] Falk undefined(1995)undefined Math. Program. 70 47-undefined
  • [10] Fukushima undefined(1998)undefined Comput. Optim. Appl. 10 5-undefined
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