Generalized parameter-free duality models in discrete minmax fractional programming based on second-order optimality conditions

Abstract

In this paper, we construct six generalized second-order parameter-free duality models, and prove several weak, strong, and strict converse duality theorems for a discrete minmax fractional programming problem using two partitioning schemes and various types of generalized second-order $$(\mathcal {F},\beta ,\phi ,\rho ,\theta ,m)$$ -univexity (more compactly, ’second-order univexity’ is referred to as ’sounivexity’) assumptions. The obtained results are new and generalize most of results on discrete minmax fractional programming involving the second-order invexity as well as on second-order univexity in the literature.