Alfred Göpfert, Hassan Riahi, Christiane Tammer

Variational Methods in Partially Ordered Spaces

• Gebundenes Buch

Produktbeschreibung

In mathematical modeling of processes occurring in logistics, management science, operations research, networks, mathematical finance, medicine, and control theory, one often encounters optimization problems involving more than one objective function so that Multiobjective Optimization (or Vector Optimization, initiated by W. Pareto) has received new impetus. The growing interest in vector optimization problems, both from the theoretical point of view and as it concerns applications to real world optimization problems, asks for a general scheme which embraces several existing developments and stimulates new ones.

This book aims to provide the newest results and applications of this quickly growing field. Basic tools of partially ordered spaces are discussed and applied to variational methods in nonlinear analysis and to optimization problems.

The book begins by providing simple examples that illustrate what kind of problems can be handled with the methods presented. The book then deals with connections between order structures and topological structures of sets, discusses properties of nonlinear scalarization functions, and derives corresponding separation theorems for not necessarily convex sets. Furthermore, characterizations of set relations via scalarization are presented.

Important topological properties of multifunctions and new results concerning the theory of vector optimization and equilibrium problems are presented in the book. These results are applied to construct numerical algorithms, especially, proximal-point algorithms and geometric algorithms based on duality assertions.

In the second edition, new sections about set less relations, optimality conditions in set optimization and the asymptotic behavior of multiobjective Pareto-equilibrium problems have been incorporated. Furthermore, a new chapter regarding scalar optimization problems under uncertainty and robust counterpart problems employing approaches based on vector optimization, set optimization, and nonlinear scalarization was added.

Throughout the entire book, there are examples used to illustrate the results and check the stated conditions.

This book will be of interest to graduate students and researchers in pure and applied mathematics, economics, and engineering. A sound knowledge of linear algebra and introductory real analysis should provide readers with sufficient background for this book.

Produktdetails

• CMS/CAIMS Books in Mathematics 7
• Verlag: Springer / Springer International Publishing / Springer, Berlin
• Artikelnr. des Verlages: 978-3-031-36533-1
• 2. Aufl.
• Seitenzahl: 584
• Erscheinungstermin: 8. Dezember 2023
• Englisch
• Abmessung: 241mm x 160mm x 37mm
• Gewicht: 1033g
• ISBN-13: 9783031365331
• ISBN-10: 303136533X
• Artikelnr.: 68099185

Autorenporträt

Professor Alfred Göpfert researched and taught at the University of Leipzig, at the Technical University of Leuna-Merseburg and at Martin-Luther-University Halle-Wittenberg (Germany). In 1973, his book "Mathematische Optimierung in allgemeinen Vektorräumen" was published by Teubner. Alfred Göpfert has co-authored the textbooks "Funktionalanalysis" (Teubner, 4th edition 1994) and "Lexikon der Optimierung - Optimierung und optimale Steuerung" (Akademie Verlag Berlin, 1986) as well as the monographs "Vektoroptimierung - Theorie, Verfahren und Anwendungen" (Teubner, 1990) and "Variational Methods in Partially Ordered Spaces" (Springer, 2003). Alfred Göpfert worked on the final version of the second edition of the monograph "Variational Methods in Partially Ordered Spaces" until his death in January 2023. Hassan Riahi received his Ph.D. degree in Applied Mathematics in 1989 at the University of Montpelier. Since 1990 he is a Professor in Applied Mathematics at the Sémlalia Faculty of Sciences at the University Cadi Ayyad in Marrakesh. His main research interests include Numerical and theoretical optimization, Variational inequalities, and Convex analysis, and he is the author of over 60 published papers and four edited books. He supervised a dozen doctoral students. Christiane Tammer is Professor at Martin-Luther-University Halle-Witten[1]berg. She is working in the fields of variational analysis and optimization. She has co-authored five monographs, i.e., "Scalarization and Separation by Translation Invariant Functions", Springer (2020); "Set-valued Optimization - An Introduction with Applications", Springer (2015); "Variational Methods in Partially Ordered Spaces", Springer (2003); "Angewandte Funktionalanalysis", Vieweg+ Teubner (2009); "Approximation und Nichtlineare Optimierung in Praxisaufgaben", Springer (2017). She is Editor-in-Chief of the journal Optimization, Co-Editor in Chief of the journal Applied Set-Valued Analysis and Optimization and a member of the Editorial Board of several journals, the Scientific Committee of the Working Group on Generalized Convexity and EUROPT Managing Board. Constantin Z¿linescu is a Professor Emeritus (Mathematics) at Alexandru Ioan Cuza University, Iäsi, Romania, and presently he is a Researcher at Octav Mayer Institute of Mathematics, Iäsi, Romania. His research interest is mainly in convex and vector optimization. He (co-)authored four books and more than 100 peer-reviewed journal articles. He has supervised 2 PhD students.

Inhaltsangabe

Examples.- Functional Analysis over Cones.- Optimization in Partially Ordered Spaces.- Applications.

Rezensionen

From the reviews: "This book is intended to provide a systematic and self-contained presentation of recent significant developments in vector optimization ... . specialists will certainly enjoy this monograph ... . On the other hand, since the book is written in a rigorous, understandable and teachable way, it may certainly serve to support courses on vector optimization, applied functional analysis, set-valued analysis, etc., targeted at the graduate level. ... As a whole, this book can be strongly recommended as an excellent reference of general interest in vector optimization." (Nicolae Popovici, Studia Universitatis Babes-Bolyai Mathematica, Vol. XLIX (4), 2004) "This book is the result of the cooperation of four known authors working in multiobjective optimization. The reader will find in this book the most important notions and results in this domain. ... We strongly recommend this book to graduate students in mathematics, economics, and engineering, and to researchers in pure and applied mathematics." (George Isac, Mathematical Reviews, 2004 h) "The book presents theory and applications of optimization problems in partially ordered spaces with emphasis on the authors' profound research results. ... The book should be a must for each scientist dealing with vector optimization theory. It delivers new insights for researchers interested in the solution of vector optimization problems. The volume can also be used as a textbook by graduate students." (Petra Weidner, MMOR - Mathematical Methods of Operations Research, June, 2004) "This exhaustive and well-written monograph represents a welcome addition to the existing optimization literature and adds favourably to any mathematical or operations research library. ... The authors take the reader on a wide-ranging journey from basic mathematical tools of partially ordered spaces to solution algorithms for some of the motivating applications ... . it balances theory and applications well. The book is written for advanced graduate students or researchers in mathematical optimization." (M Hintermueller, Journal of the Operational Research Society, Vol. 57 (11), 2006)