The book provides an introduction to multicriteria optimization. It covers theoretical topics such as existence of optimal solutions as well as methodological issues. A classification of multicriteria optimization problems is developed and used as a guideline throughout the book. First, fundamental solution concepts are defined and their properties and relations discussed. Then a variety of methods to find optimal solutions is described. Chapters on multicriteria linear optimization, uncommon solution concepts, and combinatorial problems conclude the book. The text contains material which cannot be found in other textbooks on the subject, because several chapters are based on new research results. It is suitable for a mathematically oriented course on multicriteria optimization. The material can be covered in the order in which it is presented, but it is also possible to select topics from various chapters. The exercises at the end of each chapter provide possibilities to practice as well as some outlooks to more general settings, when appropriate.
Introduction; Pareto Optimality and Efficiency; Weighted Sum Scalarization; Other Methods for Pareto Optimality; Multicriteria Linear Programming; Other Optimality Concepts; Combinatorial Problems with Multiple Objectives.