Convergence properties of a regularization scheme for mathematical programs with complementarity constraints
Convergence properties of a regularization scheme for mathematical programs with complementarity constraints
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DOI：
10.1137/s1052623499361233
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发表时间：
2001-04-24
影响因子：
3.1
通讯作者：
Scholtes, S
中科院分区：
文献类型：
--
作者：
Scholtes, S
我们研究了一个参数NLP的平稳点序列的收敛行为，该参数NLP以互补条件的形式正则化了一个具有平衡约束的数学规划（MPEC）。聚点是MPEC的可行点;如果MPEC线性独立约束条件成立，则聚点是C-平稳的;如果逼近子序列萨蒂斯二阶必要条件，则聚点是M-平稳的;如果上一级严格互补条件成立，则聚点是B-平稳的。这些结果补充了福岛和Pang的最新结果[具有平衡约束的数学规划的平滑延拓方法的收敛性，在不适定变分问题和正则化技术中，Springer-Verlag，纽约，1999年]。进一步证明了萨蒂斯线性无关、上严格互补和二阶最优性条件的MPEC局部极小点都可以嵌入到参数NLP局部极小点的局部唯一的分段光滑曲线中.
We study the convergence behavior of a sequence of stationary points of a parametric NLP which regularizes a mathematical program with equilibrium constraints (MPEC) in the form of complementarity conditions. Accumulation points are feasible points of the MPEC; they are C-stationary if the MPEC linear independence constraint qualification holds; they are M-stationary if, in addition, an approaching subsequence satis es second order necessary conditions, and they are B-stationary if, in addition, an upper level strict complementarity condition holds. These results complement recent results of Fukushima and Pang [Convergence of a smoothing continuation method for mathematical programs with equilibrium constraints, in Ill-posed Variational Problems and Regularization Techniques, Springer-Verlag, New York, 1999]. We further show that every local minimizer of the MPEC which satis es the linear independence, upper level strict complementarity, and a second order optimality condition can be embedded into a locally unique piecewise smooth curve of local minimizers of the parametric NLP.