Vector Variational Inequalities and Vector Optimization

Beschreibung

This book presents the mathematical theory of vector variational inequalities and their relations with vector optimization problems. It is the first-ever book to introduce well-posedness and sensitivity analysis for vector equilibrium problems. The first chapter provides basic notations and results from the areas of convex analysis, functional analysis, set-valued analysis and fixed-point theory for set-valued maps, as well as a brief introduction to variational inequalities and equilibrium problems. Chapter 2 presents an overview of analysis over cones, including continuity and convexity of vector-valued functions. The book then shifts its focus to solution concepts and classical methods in vector optimization. It describes the formulation of vector variational inequalities and their applications to vector optimization, followed by separate chapters on linear scalarization, nonsmooth and generalized vector variational inequalities. Lastly, the book introduces readers to vector equilibrium problems and generalized vector equilibrium problems. Written in an illustrative and reader-friendly way, the book offers a valuable resource for all researchers whose work involves optimization and vector optimization.

This book presents the mathematical theory of vector variational inequalities and their relations with vector optimization problems. It is the first-ever book to introduce well-posedness and sensitivity analysis for vector equilibrium problems. The first chapter provides basic notations and results from the areas of convex analysis, functional analysis, set-valued analysis and fixed-point theory for set-valued maps, as well as a brief introduction to variational inequalities and equilibrium problems. Chapter 2 presents an overview of analysis over cones, including continuity and convexity of vector-valued functions. The book then shifts its focus to solution concepts and classical methods in vector optimization. It describes the formulation of vector variational inequalities and their applications to vector optimization, followed by separate chapters on linear scalarization, nonsmooth and generalized vector variational inequalities. Lastly, the book introduces readers to vector equilibrium problems and generalized vector equilibrium problems. Written in an illustrative and reader-friendly way, the book offers a valuable resource for all researchers whose work involves optimization and vector optimization.

Autor*in

Qamrul Hasan Ansari

Themen in »Vector Variational Inequalities and Vector Optimization«

vector optimization vector equilibrium problems set-valued maps Ekeland's variational principle sensitivity analysis existence theory well-posedness theory of variational inequalities theory of equlibrium problems

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“This book provides a comprehensive and methodical outlook on the state of the art of this prolific field of research. The authors carefully take the reader from basic topics of nonlinear analysis (such as convexity and generalized derivatives) to analysis over cones … . The book is easy to read and provides a major reference for further research on the topic. … I am sure this book could provide useful material and ideas even for this new trend.” (Govanni Paolo Crespi, Mathematical Reviews, September, 2018)
“The goal of this book is to present the theory of vector optimization, vector variational inequalities and vector equilibrium problems. … The book offers a reach and interesting study of important subjects in the modern mathematics. It is worth mentioning the substantial efforts done by the authors to explain and motivate the concepts and results as well as to unify various topics. The monograph represents a valuable contribution to the existing literature.” (Dumitru Motreanu, zbMATH 1394.49001, 2018)
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