Bot, Radu Ioan.
Conjugate Duality in Convex Optimization [electronic resource] / by Radu Ioan Bot. - XII, 164p. online resource. - Lecture Notes in Economics and Mathematical Systems, 637 0075-8442 ; . - Lecture Notes in Economics and Mathematical Systems, 637 .
Perturbation Functions and Dual Problems -- Moreau–Rockafellar Formulae and Closedness-Type Regularity Conditions -- Biconjugate Functions -- Strong and Total Conjugate Duality -- Unconventional Fenchel Duality -- Applications of the Duality to Monotone Operators.
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.
9783642049002
10.1007/978-3-642-04900-2 doi
Mathematics.
Global analysis (Mathematics).
Systems theory.
Mathematical optimization.
Operations research.
Mathematics.
Operations Research, Mathematical Programming.
Operations Research/Decision Theory.
Optimization.
Systems Theory, Control.
Analysis.
QA402-402.37 T57.6-57.97
519.6
Conjugate Duality in Convex Optimization [electronic resource] / by Radu Ioan Bot. - XII, 164p. online resource. - Lecture Notes in Economics and Mathematical Systems, 637 0075-8442 ; . - Lecture Notes in Economics and Mathematical Systems, 637 .
Perturbation Functions and Dual Problems -- Moreau–Rockafellar Formulae and Closedness-Type Regularity Conditions -- Biconjugate Functions -- Strong and Total Conjugate Duality -- Unconventional Fenchel Duality -- Applications of the Duality to Monotone Operators.
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.
9783642049002
10.1007/978-3-642-04900-2 doi
Mathematics.
Global analysis (Mathematics).
Systems theory.
Mathematical optimization.
Operations research.
Mathematics.
Operations Research, Mathematical Programming.
Operations Research/Decision Theory.
Optimization.
Systems Theory, Control.
Analysis.
QA402-402.37 T57.6-57.97
519.6