Disjunctive Optimization: Critical Point Theory
Disjunctive Optimization: Critical Point Theory
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析取优化：临界点理论
DOI：
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发表时间：
1997
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通讯作者：
O. Stein
中科院分区：
文献类型：
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作者：
H. Jongen;J. Rückmann;O. Stein
本文引入了析取优化问题的（非退化）驻点和驻点指数的概念。证明了莫尔斯理论中的两个基本定理，这两个定理暗示了（标准）莫尔斯关系的有效性。第一个是适用于驻点集之外的变形定理。第二个是适用于非退化驻点的细胞附着定理。要附着的单元格的尺寸等于固定索引。在这里，平稳指数既取决于拉格朗日量的受限制的Hessian，也取决于活动不等式约束的集合。在标准的优化问题中，后者的贡献消失了。
In this paper, we introduce the concepts of (nondegenerate) stationary points and stationary index for disjunctive optimization problems. Two basic theorems from Morse theory, which imply the validity of the (standard) Morse relations, are proved. The first one is a deformation theorem which applies outside the stationary point set. The second one is a cell-attachment theorem which applies at nondegenerate stationary points. The dimension of the cell to be attached equals the stationary index. Here, the stationary index depends on both the restricted Hessian of the Lagrangian and the set of active inequality constraints. In standard optimization problems, the latter contribution vanishes.