Cone Quasi-Concave Multi-Objective Programming Theory and Dominance Cone Constructions

摘要

Some basic theory of cone quasi-concave multi-objective programming is developed. This new class of vector extremal problems with quasi-concave multiple objective employs ideas of nondominated solutions associated with dominance cones. Necessary as well as sufficient conditions for optimal solutions to such problems are provided. A simple example illustrates the concepts involved. In addition, for general applications in economics, it is shown how to establish dominance cones to realize producer priorities, consumer preferences, and other concerns exogenously determined. Keywords: Mathematical programming, Generalized cone concavity; Vector extremal problems; Multi objective programming, nondominated solutions. (jhd)