A nonparametric approach to nonsmooth vector fractional interval-valued optimization problems

Abstract

Interval programming is a useful tool that provides an easier way to handle uncertainty in various classes of optimization problems. Therefore, we investigate in the paper a new type of nondifferentiable vector interval-valued fractional optimization problems in which the functions involved possess a new generalized convexity property introduced in this paper for interval-valued functions. Namely, we study optimality conditions for (weak) LU-Pareto solutions of vector fractional optimization problems with interval-valued objective functions in their numerators and denominators by using the nonparametric approach. Thus, we derive both the nonparametric necessary optimality conditions of Fritz John type and, assuming additionally the Slater constraint qualification, the nonparametric type necessary optimality conditions of Karush-Kuhn-Tucker type for a feasible point of the aforesaid nonsmooth vector fractional interval-valued optimization problem to be its weakly LU-Pareto solution. The sufficient optimality conditions for a weak LU-Pareto solution and a LU-Pareto solution are also proven assuming additionally nonsmooth generalized convexity of the functions involved in the aforesaid vector optimization problem. Further, the nondifferentiable multicriteria nonparametric Mond-Weir dual problem is also formulated for the studied nondifferentiable multiobjective fractional interval-valued optimization problem. Then, dual theorems are proven for these two nondifferentiable multicriteria fractional optimization problems with interval-valued objectives in their nominators and denominators also assuming generalized convexity hypotheses.