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Fenchel-Lagrange Duality Versus Geometric Duality in Convex Optimization.

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Title: Fenchel-Lagrange Duality Versus Geometric Duality in Convex Optimization.
Authors: BOT, R. I.1, GRAD, S. M.2, WANKA, G.3
Source: Journal of Optimization Theory & Applications. Apr2006, Vol. 129 Issue 1, p33-54. 22p.
Subjects: Duality theory (Mathematics), Geometric function theory, Complex variables, Convex geometry, Convex functions, Mathematical analysis, Variational inequalities (Mathematics), Calculus of variations, Differential inequalities
Abstract: We present a new duality theory to treat convex optimization problems and we prove that the geometric duality used by Scott and Jefferson in different papers during the last quarter of century is a special case of it. Moreover, weaker sufficient conditions to achieve strong duality are considered and optimality conditions are derived. Next, we apply our approach to some problems considered by Scott and Jefferson, determining their duals. We give weaker sufficient conditions to achieve strong duality and the corresponding optimality conditions. Finally, posynomial geometric programming is viewed also as a particular case of the duality approach that we present. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Optimization Theory & Applications is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 23965069
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PubType: Academic Journal
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  Data: Fenchel-Lagrange Duality Versus Geometric Duality in Convex Optimization.
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  Data: <searchLink fieldCode="DE" term="%22Duality+theory+%28Mathematics%29%22">Duality theory (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Geometric+function+theory%22">Geometric function theory</searchLink><br /><searchLink fieldCode="DE" term="%22Complex+variables%22">Complex variables</searchLink><br /><searchLink fieldCode="DE" term="%22Convex+geometry%22">Convex geometry</searchLink><br /><searchLink fieldCode="DE" term="%22Convex+functions%22">Convex functions</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+analysis%22">Mathematical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Variational+inequalities+%28Mathematics%29%22">Variational inequalities (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Calculus+of+variations%22">Calculus of variations</searchLink><br /><searchLink fieldCode="DE" term="%22Differential+inequalities%22">Differential inequalities</searchLink>
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  Data: We present a new duality theory to treat convex optimization problems and we prove that the geometric duality used by Scott and Jefferson in different papers during the last quarter of century is a special case of it. Moreover, weaker sufficient conditions to achieve strong duality are considered and optimality conditions are derived. Next, we apply our approach to some problems considered by Scott and Jefferson, determining their duals. We give weaker sufficient conditions to achieve strong duality and the corresponding optimality conditions. Finally, posynomial geometric programming is viewed also as a particular case of the duality approach that we present. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Journal of Optimization Theory & Applications is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s10957-006-9047-2
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      – Code: eng
        Text: English
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    Subjects:
      – SubjectFull: Duality theory (Mathematics)
        Type: general
      – SubjectFull: Geometric function theory
        Type: general
      – SubjectFull: Complex variables
        Type: general
      – SubjectFull: Convex geometry
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      – SubjectFull: Convex functions
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      – SubjectFull: Mathematical analysis
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      – SubjectFull: Variational inequalities (Mathematics)
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      – SubjectFull: Calculus of variations
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      – SubjectFull: Differential inequalities
        Type: general
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      – TitleFull: Fenchel-Lagrange Duality Versus Geometric Duality in Convex Optimization.
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              Text: Apr2006
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