A Smoothing Method for a Mathematical Program with P-Matrix Linear Complementarity Constraints
A Smoothing Method for a Mathematical Program with P-Matrix Linear Complementarity Constraints
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DOI：
10.1023/b:coap.0000013057.54647.6d
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发表时间：
2004-03
影响因子：
2.2
通讯作者：
Xiaojun Chen;M. Fukushima
中科院分区：
文献类型：
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作者：
Xiaojun Chen;M. Fukushima
我们考虑一个数学程序，其约束涉及以设计（上层）变量作为参数的参数 P 矩阵线性互补问题。该互补问题的解定义了参数的分段线性函数。我们研究该函数的平滑函数来求解数学程序。我们研究了平滑问题的最优解、KKT 点和 B 平稳点的极限行为。我们证明了一类具有 P 矩阵线性互补约束的数学程序可以重新表示为分段凸程序，并通过一系列连续可微的凸程序来求解。初步数值结果表明该方法和凸重构是有前途的。
We consider a mathematical program whose constraints involve a parametric P-matrix linear complementarity problem with the design (upper level) variables as parameters. Solutions of this complementarity problem define a piecewise linear function of the parameters. We study a smoothing function of this function for solving the mathematical program. We investigate the limiting behaviour of optimal solutions, KKT points and B-stationary points of the smoothing problem. We show that a class of mathematical programs with P-matrix linear complementarity constraints can be reformulated as a piecewise convex program and solved through a sequence of continuously differentiable convex programs. Preliminary numerical results indicate that the method and convex reformulation are promising.