Continuous multiobjective programming

Wiecek, Margaret M. and Ehrgott, Matthias and Engau, Alexander (2016) Continuous multiobjective programming. In: Multiple criteria decision analysis : state of the art surveys. International Series in Operations Research & Management Science (2nd). Springer, New York, pp. 739-815. ISBN 9781493930937

Abstract

We present our view of the state of the art in continuous multiobjective programming. After an introduction we formulate the multiobjective program (MOP) and define the most important solution concepts in Sect. 18.2. In Sect. 18.3 we summarize properties of efficient and nondominated sets. Optimality conditions are reviewed in Sect. 18.4. The main part of the chapter consists of Sects. 18.5 and 18.6 that deal with solution techniques for MOPs and approximation of efficient and nondominated sets. In Sect. 18.7 we discuss specially-structured problems including linear, nonlinear, parametric, and bilevel MOPs. In Sect. 18.8 we present our perspective on future research directions.