Vector Optimization and Monotone Operators via Convex Duality

1. Front Matter

   Pages i-xvii

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2. Introduction and Preliminaries

   • Sorin-Mihai Grad

   Pages 1-11

3. Duality for Scalar Optimization Problems

   • Sorin-Mihai Grad

   Pages 13-38

4. Minimality Concepts for Sets

   • Sorin-Mihai Grad

   Pages 39-59

5. Vector Duality via Scalarization for Vector Optimization Problems

   • Sorin-Mihai Grad

   Pages 61-113

6. General Wolfe and Mond-Weir Duality

   • Sorin-Mihai Grad

   Pages 115-175

7. Vector Duality for Linear and Semidefinite Vector Optimization Problems

   • Sorin-Mihai Grad

   Pages 177-221

8. Monotone Operators Approached via Convex Analysis

   • Sorin-Mihai Grad

   Pages 223-256

9. Back Matter

   Pages 257-269

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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.

• Conjugacy
• Duality
• Monotone operators
• Representative functions
• Vector optimization

• Faculty of Mathematics, TU Chemnitz, Chemnitz, Germany

  Sorin-Mihai Grad

Sorin-Mihai Grad is currently working within the Faculty of Mathematics of Chemnitz University of Technology, Germany, where he achieved his PhD in 2006 and his Habilitation in 2014. He is co-author of the book "Duality in Vector Optimization" (Springer, 2009).

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