A generalized fractional programming problem is specified as a nonlinear program where a nonlinear function defined as the maximum over several ratios of functions is to be minimized on a feasible domain of ~n. The purpose of this paper is to outline basic approaches and basic types of algorithms available to deal with this problem and to review their convergence analysis. The conclusion includ...

The importance of linear fractional programming comes from the fact that many real life problems are based on the ratio of physical or economic values (for example cost/time, cost/volume, profit/cost or any other quantities that measure the efficiency of a system) expressed by linear functions. Usually, the coefficients used in mathematical models are subject to errors of measurement or vary wi...

We present an algorithm to solve a bi-level multi-objective fractional integer programming problem involving fuzzy numbers in the right-hand side of the constraints. The suggested algorithm combine the method of Taylor series together with the Kuhn Tucker conditions to solve fuzzy bi-level multi-objective fractional integer programming problem (FBLMOFIPP) then Gomory cuts are added till the int...

*Correspondence: [email protected] Department of Mathematics, University of Tabuk, Tabuk, Kingdom of Saudi Arabia Abstract In the present paper, we are concerned with second-order duality for nondifferentiable minimax fractional programming under the second-order generalized convexity type assumptions. The weak, strong and converse duality theorems are proved. Results obtained in this paper ext...

Three approaches of second order mixed type duality are introduced for a nondifferentiable multiobjective fractional programming problem in which the numerator and denominator of objective function contain square root of positive semidefinite quadratic form. Also, the necessary and sufficient conditions of efficient solution for fractional programming are established and a parameterization tech...

We focus our study to formulate two different types of second-order dual models for a nondifferentiable minimax fractional programming problem and derive duality theorems under (F, ρ)-convexity. Several results including many recent works are obtained as special cases.