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General Semi-Infinite Programming: Critical Point Theory

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Jongen, Hubertus Th. [RWTH Aachen University] Shikhman, Vladimir [UCL]

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.

Document type Article de périodique (Journal article) – Article de recherche
Access type Accès restreint
Publication date 2011
Language Anglais
Journal information "Optimization : a journal of mathematical programming and operations research" - Vol. 60, no. 7, p. 859-873 (2011)
Peer reviewed yes
Publisher Taylor & Francis Ltd. ((United Kingdom) Abingdon)
issn 0233-1934
e-issn 1029-4945
Publication status Publié
Affiliation UCL - SST/ICTM/INMA - Pôle en ingénierie mathématique
Links
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Bibliographic reference Jongen, Hubertus Th. ; Shikhman, Vladimir. General Semi-Infinite Programming: Critical Point Theory. In: Optimization : a journal of mathematical programming and operations research, Vol. 60, no. 7, p. 859-873 (2011)
Permanent URL http://hdl.handle.net/2078/115751