Optimality Conditions and Duality of Three Kinds of Nonlinear Fractional Programming Problems

Abstract

Some assumptions for the objective functions and constraint functions are given under the conditions of convex and generalized convex, which are based on the -convex, -convex, and ( , )-convex. The sufficiency of Kuhn-Tucker optimality conditions and appropriate duality results are proved involving ( , )-convex, ( , , , )-convex, and generalized ( , , , )-convex functions.

Optimality and duality results for E-differentiable multiobjective fractional programming problems under E-convexity

“…Using the properties of sublinear functionals and generalized convex functions, Liang et al [23] derived sufficient optimality conditions, formulated three types of duals and proved duality results for a class of nonconvex multiobjective fractional programming problems. Based on the former conclusions, by adding conditions to objective functions and constraint functions and by changing Kuhn-Tucker conditions, Zhang and Wu [43] proved the optimality conditions and duality theorems for the considered three kinds of nonlinear fractional programming problems under weaker convexity conditions. Recently, Antczak and Verma [2] proved optimality conditions and duality results for nondifferentiable multiobjective fractional programming problems under (b, Ψ , Φ, ρ)-univexity hypotheses.…”

Optimality Results for Non-Differentiable Multiobjective Fractional Programming Problems under E-B-Invexity

“…Optimality conditions and duality results for a class of (MFP) under generalized convexity assumptions using a parametric approach were established by Osuna-Gomez et al [19]. Zhang and Wu [26] established certain optimality conditions and duality results for three types of nonlinear fractional programming problems. To achieve this, they introduced additional conditions to the objective and constraint functions and modified the Karush-Kuhn-Tucker conditions.…”

Multiobjective Fractional Programming Involving Generalized Semilocally V-Type I-Preinvex and Related Functions

“…Further works on multiobjective fractional programming are established by Chinchuluun et al [17], J.-C. Liu and C.-Y. Liu [18], Mishra et al [19], Verma [20], Zhang and Wu [21], and others.…”