A Modified Relaxation Scheme for Mathematical Programs with Complementarity Constraints
A Modified Relaxation Scheme for Mathematical Programs with Complementarity Constraints
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DOI：
10.1007/s10479-004-5024-z
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发表时间：
2002-12
影响因子：
4.8
通讯作者：
G. Lin;M. Fukushima
中科院分区：
文献类型：
--
作者：
G. Lin;M. Fukushima
本文研究了一个具有互补约束的数学规划问题。我们提出了一个改进的松弛格式，它比Scholtes（2000）的松弛格式具有更少的约束条件. 在较弱的条件下, 新松弛问题满足线性独立约束规范.我们还考虑了松弛问题的一个极限行为。在MPEC线性无关约束条件下，证明了松弛问题的任一平稳点的聚集点对原问题是C-平稳的，且若松弛问题的Lagrange函数的Hessian矩阵在相应的切空间上一致有界，则是M-平稳的.我们还得到了原问题的可行点B-平稳的一些充分条件。特别地，上述Hessian矩阵的特征值所描述的一些条件是新的，并且易于验证。
In this paper, we consider a mathematical program with complementarity constraints. We present a modified relaxed program for this problem, which involves less constraints than the relaxation scheme studied by Scholtes (2000). We show that the linear independence constraint qualification holds for the new relaxed problem under some mild conditions. We also consider a limiting behavior of the relaxed problem. We prove that any accumulation point of stationary points of the relaxed problems is C-stationary to the original problem under the MPEC linear independence constraint qualification and, if the Hessian matrices of the Lagrangian functions of the relaxed problems are uniformly bounded below on the corresponding tangent space, it is M-stationary. We also obtain some sufficient conditions of B-stationarity for a feasible point of the original problem. In particular, some conditions described by the eigenvalues of the Hessian matrices mentioned above are new and can be verified easily.