This book introduces the reader to the field of multiobjective optimization through problems with simple structures, namely those in which the objective function and constraints are linear. Fundamental notions as well as state-of-the-art advances are presented in a comprehensive way and illustrated with the help of numerous examples. Three of the most popular methods for solving multiobjective linear problems are explained, and exercises are provided at the end of each chapter, helping students to grasp and apply key concepts and methods to more complex problems. The book was motivated by the fact that the majority of the practical problems we encounter in management science, engineering or operations research involve conflicting criteria and therefore it is more convenient to formulate them as multicriteria optimization models, the solution concepts and methods of which cannot be treated using traditional mathematical programming approaches.
Dinh The Luc is Distinguished Professor, Director of the Laboratory of Mathematics at Avignon University. He is also Research Fellow of the Vietnam Academy of Science and Technology. He was graduated from Lomonosov Moscow State University in 1974 and received his PhD from the Hungarian Academy of Sciences in 1983. His research interests center on vector optimization, nonsmooth analysis, set-valued analysis and multi-criteria transportation network. His monograph "Theory of Vector Optimization" published by Springer in 1989 is one of the most cited books in this area. He is also co-author with V. Jeyakumar of "Nonsmooth Vector Functions and Continuous Optimization" (Springer 2008).
Part I: Background.- Part II: Theory.- Part III: Methods.