The issue of characterizing completely efficient (Pareto) solutions to a fractional vector (multiobjective or multicriteria) minimization problem, where the involved functions are convex, has not been addressed previously. Thanks to an earlier characterization of weak efficiency in difference vector optimization by El Maghri, we get a vectorial necessary and sufficient condition given in terms of both strong (Fenchel) and weak (Pareto) vector ε-subdifferentials that completely characterizes the exact or approximate weak efficiency in fractional multiobjective optimization. Moreover, this result applies not only for unconstrained problems but also for convex constrained problems, where in the first case no assumption of convexity is required, while in the second case only the numerators need to be convex. When the fractional problem is to minimize the ratios of convex functions by concave functions, simpler vectorial characterizations for exact or approximate proper or weak efficiency are also developed. Finally, application to the particular case of linear fractional multiobjective programs also provides new results.
Hassan II University, Casablanca, Morocco