Semi-continuous quadratic optimization: existence conditions and duality scheme

In this work, we study the class of problems called semi-continuous optimization, which contains constrained minimization (maximization) problems with lower (upper) semi-continuous objective functions. We show some existence conditions for solutions based on asymptotic techniques, as well as a duali...

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Bibliographic Details
Published inJournal of global optimization Vol. 63; no. 2; pp. 281 - 295
Main Authors Cotrina, John, Raupp, Fernanda M. P., Sosa, Wilfredo
Format Journal Article
LanguageEnglish
Published New York Springer US 01.10.2015
Springer
Springer Nature B.V
Subjects
Asymptotic methods
Asymptotic properties
Computer Science
Conjugation
Constraints
Mathematical models
Mathematics
Mathematics and Statistics
Maximization
Minimization
Operations Research/Decision Theory
Optimization
Optimization techniques
Quadratic equations
Real Functions
Recessions
Studies
Symmetry
90C20
Semi-continuous optimization
90C46
Existence conditions
Fenchel–Moreau conjugation
90C26
Duality scheme
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Summary:In this work, we study the class of problems called semi-continuous optimization, which contains constrained minimization (maximization) problems with lower (upper) semi-continuous objective functions. We show some existence conditions for solutions based on asymptotic techniques, as well as a duality scheme based on the Fenchel–Moreau conjugation specifically applied to semi-continuous problems. Promising results are obtained, when we apply this scheme to minimize quadratic functions (whose Hessians can be symmetric indefinite) over nonempty, closed and convex polyhedral sets.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-015-0306-3