Vector Variational Inequalities and Vector Optimization: Theory and Applications

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Beschreibung

Pressestimmen

“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, Monat des Herbstbeginns, 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 Studierender of important subjects in the trendig mathematics. It is worth mentioning the substantial efforts done by the authors to explain and motivate the concepts and results as well as to nicht various topics. The monograph represents a valuable contribution to the existing literature.” (Dumitru Motreanu, zbMATH 1394.49001, 2018)

Buchrückseite

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, sine temporevalued analysis and fixed-point theory for sine temporevalued 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 eindimensional scalarization, nonsmooth and generalized vector variational inequalities. Lastly, the book introduces readers to vector equilibrium problems and generalized vector equilibrium problems. Written non… illustrative and reader-friendly way, the book offers a valuable resource for all researchers whose work involves optimization and vector optimization.

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