On non linear scalarization in vector optimization

For a multiobjective concave optimization problem P linear scalarization holds in the sense that an efficient point for problem P turns out to be an optimal solution of a scalar problem whose objective function is a suitable weighted sum of objective functions of P. Since this nice property does not hold when P is not concave, in this paper we will consider a scalar parametric problem of exponential kind P(λ, μ) with two parameters λ, μ and we will find conditions under which an efficient point for P is an optimal solution for P(λ, μ). The suggested approach based on separation between two suitable sets allow us to obtain nonlinear scalarization for wide classes of problems containing some subclasses of generalized concave problem