Variational Methods in Partially Ordered Spaces

by Alfred Gïpfert, Hassan Riahi, Christiane Tammer, Constantin Zalinescu

Overview

In mathematical modeling of processes one often encounters optimization problems involving more than one objective function, so that Multiobjective Optimization (or Vector Optimization) has received new impetus. The growing interest in multiobjective problems, both from the theoretical point of view and as it concerns applications to real problems, asks for a general scheme which embraces several existing developments and stimulates new ones. In this book the authors provide the newest results and applications of this quickly growing field. This book will be of interest to graduate students in mathematics, economics, and engineering, as well as researchers in pure and applied mathematics, economics, engineering, geography, and town planning. A sound knowledge of linear algebra and introductory real analysis should provide readers with sufficient background for this book.

Product Details

ISBN-13:	9783031365348
Publisher:	Springer-Verlag New York, LLC
Publication date:	12/08/2023
Series:	CMS/CAIMS Books in Mathematics , #7
Sold by:	Barnes & Noble
Format:	eBook
File size:	88 MB
Note:	This product may take a few minutes to download.

About the Author

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 Zălinescu is a Professor Emeritus (Mathematics) at Alexandru Ioan Cuza University, Ia¸si, Romania, and presently he is a Researcher at Octav Mayer Institute of Mathematics, Ia¸si, 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.

Table of Contents

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

Editorial Reviews

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 andapplications 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)

From the Publisher