Vector Optimization and Monotone Operators via Convex Duality

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Cover of the book Vector Optimization and Monotone Operators via Convex Duality by Sorin-Mihai Grad, Springer International Publishing
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Author: Sorin-Mihai Grad ISBN: 9783319089003
Publisher: Springer International Publishing Publication: September 3, 2014
Imprint: Springer Language: English
Author: Sorin-Mihai Grad
ISBN: 9783319089003
Publisher: Springer International Publishing
Publication: September 3, 2014
Imprint: Springer
Language: English

This book investigates several duality approaches for vector optimization problems, while also comparing them. Special attention is paid to duality for linear vector optimization problems, for which a vector dual that avoids the shortcomings of the classical ones is proposed. Moreover, the book addresses different efficiency concepts for vector optimization problems. Among the problems that appear when the framework is generalized by considering set-valued functions, an increasing interest is generated by those involving monotone operators, especially now that new methods for approaching them by means of convex analysis have been developed. Following this path, the book provides several results on different properties of sums of monotone operators.

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This book investigates several duality approaches for vector optimization problems, while also comparing them. Special attention is paid to duality for linear vector optimization problems, for which a vector dual that avoids the shortcomings of the classical ones is proposed. Moreover, the book addresses different efficiency concepts for vector optimization problems. Among the problems that appear when the framework is generalized by considering set-valued functions, an increasing interest is generated by those involving monotone operators, especially now that new methods for approaching them by means of convex analysis have been developed. Following this path, the book provides several results on different properties of sums of monotone operators.

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