Duality in Vector Optimization

This book presents fundamentals and comprehensive results regarding duality for scalar, vector and set-valued optimization problems in a general setting. After a preliminary chapter dedicated to convex analysis and minimality notions of sets with respect to partial orderings induced by convex cones a chapter on scalar conjugate duality follows. Then investigations on vector duality based on scalar conjugacy are made. Weak, strong and converse duality statements are delivered and connections to classical results from the literature are emphasized. One chapter is exclusively consecrated to the scalar and vector Wolfe and Mond-Weir duality schemes. The monograph is closed with extensive considerations concerning conjugate duality for set-valued optimization problems.

List of contents

Preliminaries on convex analysis and vector optimization.- Conjugate duality in scalar optimization.- Conjugate vector duality via scalarization.- Conjugate duality for vector optimization problems with finite dimensional image spaces.- Wolfe and Mond-Weir duality concepts.- Duality for set-valued optimization problems based on vector conjugacy.

Summary

This book presents fundamentals and comprehensive results regarding duality for scalar, vector and set-valued optimization problems in a general setting. One chapter is exclusively consecrated to the scalar and vector Wolfe and Mond-Weir duality schemes.

Additional text

From the reviews:
“This book is dedicated to duality in vector optimization and is largely based on the contribution of the authors to this field. The book is divided into 7 chapters; it also contains a list of symbols and notations, an index of terms and a bibliography with 210 titles. … We recommend this book to researchers in convex scalar and vector optimization.” (Constantin Zălinescu, Mathematical Reviews, Issue 2010 i)

Report

From the reviews:
"This book is dedicated to duality in vector optimization and is largely based on the contribution of the authors to this field. The book is divided into 7 chapters; it also contains a list of symbols and notations, an index of terms and a bibliography with 210 titles. ... We recommend this book to researchers in convex scalar and vector optimization." (Constantin Zalinescu, Mathematical Reviews, Issue 2010 i)

Product details

• Authors: Radu Ioa Bot, Radu Ioan Bot, Sorin-Miha Grad, Sorin-Mihai Grad, Radu Ioan-Bot, Gert Wanka
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 08.12.2011
• EAN: 9783642269363
• ISBN: 978-3-642-26936-3
• No. of pages: 400
• Weight: 628 g
• Illustrations: XVI, 400 p.
• Series: Vector Optimization; Vector Optimization
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Probability theory, stochastic theory, mathematical statistics; Operations Research, B, Operations Research/Decision Theory, Operations Research and Decision Theory, Mathematics and Statistics, Management & management techniques, Operations Research, Management Science, Discrete Mathematics in Computer Science, Discrete Mathematics, Management decision making, Management science, Operational research, Decision Making, Computer science—Mathematics, Maths for computer scientists, Maths for engineers, Mathematical Modeling and Industrial Mathematics, Mathematical models