Optimality and Duality for a Class of Nondifferentiable Multiobjective Fractional Programming Problems

Optimality and Duality for Nondifferentiable Fractional Programming With Generalized Invexity

“…Many authors have introduced various concepts of generalized convexity and have obtained optimality and duality results for optimization programming problem ( [1]- [4], [6]- [12]). Many practical problems encountered in economics, engineering design, and management science, and so forth can be described by nonsmooth functions.…”

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.…”

Generalized Lagrange Function and Generalized Weak Saddle Points for a Class of Multiobjective Fractional Optimal Control Problems

“…Recently, many authors studied the efficiency and optimality conditions for multiobjective optimal control problems [1][2][3][4][5][6]. Other authors considered optimality and duality for fractional programming problems [7][8][9]. The Lagrange multipliers of multiobjective programming problems, and the saddle points of their vector-valued Lagrangian function, have been studied in [10][11][12][13][14].…”