Parameter-free duality models and applications to semiinfinite minmax fractional programming based on second-order ( $$\phi ,\eta ,\rho ,\theta ,{\tilde{m}}$$ ϕ , η , ρ , θ , m ~ )-sonvexities

Abstract

A class of second order parameter-free duality models are constructed for semiinfinite (with infinitely many inequality and equality constraints) discrete minmax fractional programming problems, and then using various generalized second-order ( $$\phi ,\eta ,\rho ,\theta ,{\tilde{m}}$$ )-sonvexity frameworks, several weak, strong, and strictly converse duality theorems are established. The semiinfinite fractional programming is a rapidly fast-expanding research field, and whose real-world applications range from the robotics to money market portfolio management, while duality models and duality theorems developed in this paper encompass most of the results on the generalized fractional programming problems (with finite number of constraints), not just for parameter-free duality results but beyond in the literature. To the best of our knowledge, the obtained parameter-free duality results are new, and more importantly are highly significant to the context of the semiinfinite aspects of the fractional programming in terms of interdisciplinary applications.