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.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)"In this book, basic tools of partially ordered spaces are discussed and applied to variational methods in nonlinear analysis and to optimization problems. The authors begin by providing simple examples that illustrate what kind of problems can be handled with the methods of the book. They then deal with connections between order structures and topological structures of sets, give a new nonconvex separation theorem, and study different properties of multifunctions. Next, the authors present new results concerning the theory of multicriteria optimization and equilibrium problems directly. In the final chapter, these results are applied in order to construct numerical algorithms, especially proximal-point algorithms and geometric algorithms based on duality assertions. Concrete applications with solution procedures are discussed, along with corresponding software. 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 interested in pure and applied mathematics, economics, and engineering. All that is required is a sound knowledge of linear algebra and introductory real analysis. While this book contains much new research, the material is presented in a clear, and teachable manner."--BOOK JACKET. Title Summary field provided by Blackwell North America, Inc. All Rights Reserved
show more show less