Vector Optimization

Vector optimization is the discipline that studies the approaches for selecting optimal decisions from a given admissible (feasible) set in the presence of two (bicriteria) or more (multicriteria) conflicting objectives (see also, for example, Ehrgott (2005) Multicriteria optimization, 2nd edn. Springer, Berlin; Jahn (1986) Mathematical vector optimization in partially ordered linear spaces. P. Lang, Frankfurt am Main; Jahn (2011) Vector optimization: theory, applications and extensions. Springer; Luc (1989) Theory of vector optimization. Springer, Berlin; Sawaragi et al. (1985) Theory of multiobjective optimization. Academic, New York). The increasing interest, in the last decades, toward this discipline is mainly due to the fact that, in optimization processes, it seems more realistic to accept the presence of more than one objective. This, in fact, happens in economic systems (maximization of the profit and minimization of the risk in portfolio selection problems), engineering systems, and physical systems (see, for example, Stadler (1984) Appl Mech Rev 37(3):277–286) and so on. To optimize one objective function is very different with respect to optimize more than one (see, for example, [3, 4, 12])