Duality in nondifferentiable minimax fractional programming with B-(p, r)- invexity

Abstract

In this article, we are concerned with a nondifferentiable minimax fractional programming problem. We derive the sufficient condition for an optimal solution to the problem and then establish weak, strong, and strict converse duality theorems for the problem and its dual problem under B-(p, r)-invexity assumptions. Examples are given to show that B-(p, r)-invex functions are generalization of (p, r)-invex and convex functions

Weakly fuzzy efficient conditions for multiobjective fractional programming problem

“…which contradict the efficiency of x o for MOFP (2). On the other hand, there exist x ∈ S with aspiration levels (g i , t i ) such that…”

“…Then, x o is an optimal solution for a weighting problem withλ i ∈ W. So, by Theorem (1), x o is weakly fuzzy efficient for FMOFP(3) and from the theorem (1) also weakly efficient for MOFP (2). Now next various necessary and sufficient conditions are established for optimal solutions under differentiability assumptions.…”

“…In (2011), Ahmad et al [2] studied about a non differentiable minimax fractional programming problem. They have proved weak, strong and strict converse duality theorems for the problem.…”

“…Weir [38] and Singh [34] have consid-ered multiobjective non-linear fractional programming problems and have obtained the dual problems by transforming the problems through generalized Charnes or Schaible transformations. Many researchers studied the optimality conditions for multiobjective fractional programming problem under generalized convexity [2,3,5,6]. But in most of these, there is no fuzzy efficient optimality conditions, because, goals and tolerance limits are assumed in classical sense in all the past approaches.…”

Mixed type duality in non-differentiable multi-objective fractional programming under generalised (Φ, ρ)-univex function

“…in order to measure the efficiency or productivity of the system. Many economic, non-economic and indirect applications of fractional programming problem have also been given by Dinklebaeh (1967), Jagannathan (1973), Bector (1973), Bector and Chandra (1986), Craven (1998), Mond and Weir (1982), Stancu-Minasian (1997), Schaible and Ibaraki (1983), Ahmad and Sharma (2007), Gulati et al (2007), Kim et al (2006) and Ahmad et al (2011aAhmad et al ( , 2011b.…”