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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Published in | Journal of global optimization Vol. 63; no. 2; pp. 281 - 295 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
New York
Springer US
01.10.2015
Springer Springer Nature B.V |
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Abstract | 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. |
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AbstractList | 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. |
Audience | Academic |
Author | Cotrina, John Sosa, Wilfredo Raupp, Fernanda M. P. |
Author_xml | – sequence: 1 givenname: John surname: Cotrina fullname: Cotrina, John organization: Universidad del Pacífico – sequence: 2 givenname: Fernanda M. P. surname: Raupp fullname: Raupp, Fernanda M. P. email: fernanda@lncc.br organization: Departamento de Engenharia Industrial, Pontifícia Universidade Católica do Rio de Janeiro, Laboratório Nacional de Computação Científica – sequence: 3 givenname: Wilfredo surname: Sosa fullname: Sosa, Wilfredo organization: Programa de Pós-Graduação em Economia, Universidade Católica de Brasília |
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Cites_doi | 10.1080/02331939508844059 10.1016/S0362-546X(02)00154-2 10.1137/0315022 10.1080/02331934.2010.507273 10.1007/BF00282202 10.1137/0316018 10.1007/s10107-013-0647-y 10.1080/02331934.2010.524217 10.1007/s10107-007-0125-5 10.1016/0362-546X(94)00364-N 10.1137/050647621 10.1023/A:1025512021335 10.1007/978-3-642-02431-3 10.1287/moor.21.4.769 10.1007/0-387-23393-8_6 |
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Keywords | 90C20 Semi-continuous optimization 90C46 Existence conditions Fenchel–Moreau conjugation 90C26 Duality scheme |
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References_xml | – volume: 49 start-page: 109 year: 1970 ident: 306_CR13 publication-title: J. Math. Pure Appl. contributor: fullname: J-J Moreau – volume: 33 start-page: 1 year: 1995 ident: 306_CR17 publication-title: Optimization doi: 10.1080/02331939508844059 contributor: fullname: F Flores-Bazán – volume: 52 start-page: 621 year: 2003 ident: 306_CR6 publication-title: Nonlinear Anal. Theory Methods Appl. doi: 10.1016/S0362-546X(02)00154-2 contributor: fullname: AN Iusem – volume: 15 start-page: 329 year: 1977 ident: 306_CR14 publication-title: SIAM J. Control Optim. doi: 10.1137/0315022 contributor: fullname: EJ Balder – volume: 60 start-page: 1045 year: 2011 ident: 306_CR12 publication-title: Optimization doi: 10.1080/02331934.2010.507273 contributor: fullname: J Cotrina – volume: 100 start-page: 149 year: 1988 ident: 306_CR5 publication-title: Arch. Ration. Mech. Anal. doi: 10.1007/BF00282202 contributor: fullname: C Baiocchi – volume-title: Asymptotic Cones and Functions in Optimization and Variational Inequalities year: 2003 ident: 306_CR1 contributor: fullname: A Auslender – volume: 16 start-page: 277 year: 1978 ident: 306_CR16 publication-title: J. Control Optim. doi: 10.1137/0316018 contributor: fullname: S Dolecki – volume: 16 start-page: 807 year: 2009 ident: 306_CR20 publication-title: J. Convex Anal. contributor: fullname: AN Iusem – volume-title: Nonconvex Optimization and its Applications year: 2005 ident: 306_CR7 contributor: fullname: GM Lee – volume: 145 start-page: 263 year: 2014 ident: 306_CR21 publication-title: Math. Program. Ser. A doi: 10.1007/s10107-013-0647-y contributor: fullname: F Flores-Bazan – volume: 60 start-page: 1209 year: 2011 ident: 306_CR11 publication-title: Optimization doi: 10.1080/02331934.2010.524217 contributor: fullname: BF Svaiter – volume: 116 start-page: 259 year: 2009 ident: 306_CR19 publication-title: Math. Program. Ser. B doi: 10.1007/s10107-007-0125-5 contributor: fullname: AN Iusem – volume: 26 start-page: 1573 year: 1996 ident: 306_CR3 publication-title: Nonlinear Anal. Theory Methods Appl. doi: 10.1016/0362-546X(94)00364-N contributor: fullname: S Adler – volume-title: Convex Analysis and Optimization year: 2003 ident: 306_CR8 contributor: fullname: D Bertsekas – volume: 18 start-page: 413 year: 2007 ident: 306_CR15 publication-title: SIAM J. Optim. doi: 10.1137/050647621 contributor: fullname: RS Burachik – volume-title: Convex Analysis, Princeton Mathematical Series, No. 28 year: 1970 ident: 306_CR2 contributor: fullname: RT Rockafellar – ident: 306_CR9 doi: 10.1023/A:1025512021335 – ident: 306_CR18 doi: 10.1007/978-3-642-02431-3 – volume: 21 start-page: 769 year: 1996 ident: 306_CR4 publication-title: Math. Oper. Res. doi: 10.1287/moor.21.4.769 contributor: fullname: A Auslender – ident: 306_CR10 doi: 10.1007/0-387-23393-8_6 |
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SubjectTerms | 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 |
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