General semi-infinite programming: critical point theory
| Autor: | Hubertus Th. Jongen, Vladimir Shikhman |
|---|---|
| Rok vydání: | 2011 |
| Předmět: |
Discrete mathematics
Connected component Control and Optimization Karush–Kuhn–Tucker conditions Optimization problem Applied Mathematics Mathematics::Optimization and Control Management Science and Operations Research Semi-infinite programming Critical point (mathematics) Invariant (mathematics) Ansatz Mathematics Morse theory |
| Zdroj: | Optimization. 60:859-873 |
| ISSN: | 1029-4945 0233-1934 |
| DOI: | 10.1080/02331934.2010.543134 |
| Popis: | We study General Semi-Infinite Programming (GSIP) from a topological point of view. Under the Symmetric Mangasarian-Fromovitz Constraint Qualification (Sym-MFCQ) two basic theorems from Morse theory (deformation theorem and cell-attachment theorem) are proved. Outside the set of Karush-Kuhn-Tucker (KKT) points, continuous deformation of lower level sets can be performed. As a consequence, the topological data (such as the number of connected components) then remain invariant. However, when passing a KKT level, the topology of the lower level set changes via the attachment of a q-dimensional cell. The dimension q equals the so-called GSIP-index of the (nondegenerate) KKT-point. Here, the Nonsmooth Symmetric Reduction Ansatz (NSRA) allows to perform a local reduction of GSIP to a Disjunctive Optimization Problem. The GSIP-index then coincides with the stationary index from the corresponding Disjunctive Optimization Problem. |
| Databáze: | OpenAIRE |
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