Vector Variational Inequalities and Vector Optimization

Qamrul Hasan Ansari is Professor of Mathematics at Aligarh Muslim University, India. His research interest lies in applied functional analysis, optimization, convex analysis, nonlinear analysis, fixed point theory in topological vector spaces, abstract economies and game theory. He looks back at 28 years of teaching and research experience and is co-author of two further books and editor/co-editor of seven books. Elisabeth Koebis is lecturer and researcher at Martin-Luther-University Halle-Wittenberg, Germany. She received her PhD from Martin-Luther-University Halle-Wittenberg, Germany. Her research interest lies in set optimization, vector optimization, robust and uncertain optimization, robust approaches to uncertain multi-objective optimization problems and unified approaches to uncertain optimization using nonlinear scalarization. Jen-Chih Yao is professor at the Center for General Education at China Medical University, Taichung, Taiwan, and at the Department of Applied Mathematics at National Sun Yat-sen University, Kaohsiung, Taiwan. He received the Outstanding Contribution Award of The Mathematical Society of the Republic of China in 2011, and has consecutively been recognized as a Highly Cited Researcher by Thomson Reuters in the years 2011 - 2016. His research interest lies in vector optimization, fixed point theory, variational inequalities, complementarity problems, variational analysis, equilibrium problems, optimal control, and generalized convexity and generalized monotonicity.

Preliminaries.- Analysis over Cones.- Solution Concepts in Vector Optimization.- Classical Methods in Vector Optimization.- Vector Variational Inequalities.- Linear Scalarization of Vector Variational Inequalities.- Nonsmooth Vector Variational Inequalities.- Generalized Vector Variational Inequalities.- Vector Equilibrium Problems.- Generalized Vector Equilibrium Problems.

"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)