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Conjugate Duality in Convex Optimization / by Radu Ioan Bot
Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: SpringerLink Bücher | Lecture notes in economics and mathematical systems ; 637Publisher: Berlin, Heidelberg : Springer-Verlag Berlin Heidelberg, 2010Description: Online-Ressource (XII, 164p, online resource)ISBN:- 9783642049002
- 1282834940
- 9783642048999
- 9781282834941
- Nichtlineare Optimierung
- Duales Optimierungsproblem
- Theorie
- Konvexe Optimierung
- Konjugierte Dualität
- Decision making
- Management science
- System theory
- Mathematical analysis
- Analysis (Mathematics)
- Global analysis (Mathematics)
- Mathematical optimization
- Mathematics
- Operations research
- Systems theory
- Convex functions
- Duality theory (Mathematics)
- Mathematical optimization
- Monotone operators
- 519.6
- QA402-402.37 T57.6-57.97
- QA402.5
Contents:
Summary: Perturbation Functions and Dual Problems -- Moreau#x2013;Rockafellar Formulae and Closedness-Type Regularity Conditions -- Biconjugate Functions -- Strong and Total Conjugate Duality -- Unconventional Fenchel Duality -- Applications of the Duality to Monotone Operators.Summary: This book presents new achievements and results in the theory of conjugate duality for convex optimization problems. The perturbation approach for attaching a dual problem to a primal one makes the object of a preliminary chapter, where also an overview of the classical generalized interior point regularity conditions is given. A central role in the book is played by the formulation of generalized Moreau-Rockafellar formulae and closedness-type conditions, the latter constituting a new class of regularity conditions, in many situations with a wider applicability than the generalized interior point ones. The reader also receives deep insights into biconjugate calculus for convex functions, the relations between different existing strong duality notions, but also into several unconventional Fenchel duality topics. The final part of the book is consecrated to the applications of the convex duality theory in the field of monotone operators.PPN: PPN: 164881154XPackage identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SXMS | ZDB-2-SMA
Conjugate Duality in Convex Optimization; Introduction; I Perturbation Functions and Dual Problems; II Moreau-Rockafellar Formulae and Closedness-Type Regularity Conditions; III Biconjugate Functions; IV Strong and Total Conjugate Duality; V Unconventional Fenchel Duality; VI Applications of the Duality to Monotone Operators; References; Index
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