Balanced states in vector optimization problems (Q2266671)

One investigates the problem of determining Pareto points, satisfying additional conditions of the equality type. One proves a theorem on the existence of solutions. Examples are given. The purpose of this paper is to present a natural formulation of the problem of vector optimization which, in spite of the abundant literature regarding this question, has not been considered so far in the general form. It has arisen from the tendency to unify the proofs of a series of theorems on the existence of an optimal distribution of the resources under nonuniform prices. However, there exist also other examples where one can apply the approach described here; one of them is contained in the last section of the paper.