Conjugate Duality in Convex Optimization
Bot, Radu Ioan.
creator
author.
SpringerLink (Online service)
text
gw
2010
monographic
eng
access
XII, 164 p. online resource.
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.
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.
by Radu Ioan Bot.
Mathematics
Operations research
Decision making
Mathematical analysis
Analysis (Mathematics)
System theory
Mathematical optimization
Management science
Mathematics
Operations Research, Management Science
Operation Research/Decision Theory
Optimization
Systems Theory, Control
Analysis
QA402-402.37
T57.6-57.97
519.6
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