Vector Variational Inequalities and Vector Optimization / Vector Optimization (PDF)
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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.
Elisabeth Köbis 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.
- Autoren: Qamrul Hasan Ansari , Elisabeth Köbis , Jen-Chih Yao
- 2017, 1st ed. 2018, 509 Seiten, Englisch
- Verlag: Springer-Verlag GmbH
- ISBN-10: 3319630490
- ISBN-13: 9783319630496
- Erscheinungsdatum: 31.10.2017
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“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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