Quasi-concave multiple objective programming with cone structure

In this paper, some basic theory of ‘cone quasi-concave multiple objective programming’ is developed. This new class of multiple objective programming problems employs ideas of nondominated solutions associated with dominance cones. Necessary as well as sufficient conditions for nondominated solutions of such problems are provided. Aside from these, in order to find a nondominated solution, the authors partition all the objectives into several mutually exclusive subgroups and assume that the weighted sum of the objectives in each subgroup is quasi-concave for the given weights. This is different from the assumption in the existing multiple objective programming literature that the weighted sum of all the objective functions is quasiconcave.