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Vector optimization and monotone ope...

Grad, Sorin-Mihai, (1979-)

Vector optimization and monotone operators via convex duality : = recent advances /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Vector optimization and monotone operators via convex duality :/ Sorin-Mihai Grad.
其他題名:	recent advances /
作者:	Grad, Sorin-Mihai,
出版者:	Cham :Springer, : c2015.,
面頁冊數:	xvii, 269 p. ;25 cm.;
標題:	Mathematical optimization. -
ISBN:	3319088998

Vector optimization and monotone operators via convex duality : = recent advances /
Grad, Sorin-Mihai,1979-

Vector optimization and monotone operators via convex duality :recent advances /Sorin-Mihai Grad. - Cham :Springer,c2015. - xvii, 269 p. ;25 cm. - Vector optimization. - Vector optimization..

Includes bibliographical references (p. 257-266) and index.

1. Introduction and preliminaries -- 2. Duality for scalar optimization problems -- 3. Minimality concepts for sets -- 4. Vector duality via scalarization for vector optimization problems -- 5. General Wolfe and Mond-Weir duality -- 6. Vector duality for linear and semidefinite vector optimization problems -- 7. Monotone operators approached via convex analysis.

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.

ISBN: 3319088998Subjects--Topical Terms:

527675
Mathematical optimization.

LC Class. No.: QA402.5 / .G7233 2015

Dewey Class. No.: 519.6

Vector optimization and monotone operators via convex duality : = recent advances /
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504 $a Includes bibliographical references (p. 257-266) and index.
505 0 # $a 1. Introduction and preliminaries -- 2. Duality for scalar optimization problems -- 3. Minimality concepts for sets -- 4. Vector duality via scalarization for vector optimization problems -- 5. General Wolfe and Mond-Weir duality -- 6. Vector duality for linear and semidefinite vector optimization problems -- 7. Monotone operators approached via convex analysis.
520 3 $a 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.
650 # 0 $a Mathematical optimization. $3 527675
650 # 0 $a Vector spaces. $3 528614
650 # 0 $a Duality theory (Mathematics) $3 527743
650 # 0 $a Convex functions. $3 527742
830 0 $a Vector optimization. $3 881449