($\epsilon$-)efficiency in multicriteria fractional optimization

The issue of characterizing completely the efficient (Pareto) solutions to a multicriteria (or multiobjective) fractional minimization problem, when the involved functions are convex, has not been addressed previously in the literature.Thanks to an earlier characterization of weak (-)efficiency in difference vector optimization by El Maghri, a similar condition given in terms of both strong (Fenchel) and weak (Pareto) -subdifferentials is first obtained for general unconstrained multicriteria fractional problems.Next, this condition is extended to constrained problems whose numerators and constraints are convex.When the fractional problem consists of minimizing ratios of convex functions by concave functions, KKT-type vector characterizations are developed for both proper and weak (-)efficiency.Finally, applications to the special all-linear case lead to (-)efficiency criteria given entirely in terms of the data.