Discrete Minmax Fractional Programming Research Articles

New Class of Duality Models in Discrete Minmax Fractional Programming Based on Second-Order Univexities

The main goal of this paper is first to formulate four new general higher order parametric duality models for a discrete minmax fractional programming problem, and then prove appropriate duality theorems applying various new classes of second order univex functions.

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

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.

Higher-order parameter-free sufficient optimality conditions in discrete minmax fractional programming

The purpose of this paper is to establish a fairly large number of sets of second-order parameter-free sufficient optimality conditions for a discrete minmax fractional programming problem. Our effort to accomplish this goal is by utilizing various new classes of generalized second-order $(\phi,\eta,\rho,\theta,m)$-invex functions, which generalize most of the concepts available in the literature.

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

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.

Generalized Second-Order Parametric Optimality Conditions in Semiinfinite Discrete Minmax Fractional Programming and Second-Order Univexity

This paper deals with mainly establishing numerous sets of generalized second order paramertic sufficient optimality conditions for a semiinfinite discrete minmax fractional programming problem, while the results on semiinfinite discrete minmax fractional programming problem achieved based on some partitioning schemes under various types of generalized second order univexity assumptions.

Generalized Higher Order (φ, η, ω, π, ρ, θ, m)-Invexities in Parametric Optimality Conditions for Discrete Minmax Fractional Programming

First several new classes of higher order (φ, η, ω, π, ρ, θ, m)-invexities are introduced, and then a set of higher-order parametric necessary optimality conditions and several sets of higher order sufficient optimality conditions for a discrete minmax fractional programming problem applying various higher order (φ, η, ω, π, ρ, θ, m)-invexity constraints are established. The obtained results are new and generalize a wide range of results in the literature.

Parametric Duality Models for Semi-infinite Discrete Minmax Fractional Programming Problems Involving Generalized (η,ρ)-Invex Functions

In this paper, we discuss a fairly large number of nonparametric duality results under various generalized (η, ρ)-invexity assumptions for a semi-infinite minmax fractional programming problem.

Parametric duality models for discrete minmax fractional programming problems containing generalized (θ,η,ρ)-V- invex functions and arbitrary norms

The purpose of this paper is to construct several parametric duality models and prove appropriate duality results under various generalized (θ, η, ρ)-V-invexity assumptions for a discrete minmax fractional programming problem involving arbitrary norms.

Global Parametric Sufficient Optimality Conditions for Semi-infinite Discrete Minmax Fractional Programming Problems Involving Generalized (η,ρ)-invex Functions

In this paper, we establish a set of necessary optimality conditions and discuss a fairly large number of sets of global nonparametric sufficient optimality criteria under various generalized (η, ρ)-invexity assumptions for a minmax fractional programming problem with infinitely many nonlinear inequality and equality constraints.

Global Nonparametric Sufficient Optimality Conditions for Semi-Infinite Discrete Minmax Fractional Programming Problems Involving Generalized (η, ρ)-Invex Functions

In this paper, we establish a set of necessary optimality conditions and discuss a fairly large number of sets of global nonparametric sufficient optimality criteria under various generalized (η, ρ)-invexity assumptions for a minmax fractional programming problem with infinitely many nonlinear inequality and equality constraints.

Nonparametric Duality Models for Semi-Infinite Discrete Minmax Fractional Programming Problems Involving Generalized (η, ρ)-Invex Functions

In this paper, we discuss a fairly large number of nonparametric duality results under various generalized (η, ρ)-invexity assumptions for a semi-infinite minmax fractional programming problem.

Global parametric sufficient optimality conditions for discrete minmax fractional programming problems containing generalized (θ, η, ρ)-V-invex functions and arbitrary norms

The purpose of this paper is to develop a fairly large number of sets of global parametric sufficient optimality conditions under various generalized(θ, η, ρ)-V-invexity assumptions for a discrete minmax fractional programming problem involving arbitrary norms.

Parametric sufficient optimality conditions and duality models for minmax fractional subset programming problems with generalized (F, ρ, θ) -convex functions

In this paper we present numerous sets of global parametric sufficient optimality conditions and duality results under various generalized (F, ρ, θ) -convexity assumptions for a discrete minmax fractional subset programming problem.