On generalised convex mathematical programming

Abstract

The sufficient optimality conditions and duality results have recently been given for the following generalised convex programming problem:where the functions / and g satisfyIt is shown here that a relaxation defining the above generalised convexity leads to a new class of multi-objective problems which preserves the sufficient optimality and duality results in the scalar case, and avoids the major difficulty of verifying that the inequality holds for the same function rj (., .). Further, this relaxation allows one to treat certain nonlinear multi-objective fractional programming problems and some other classes of nonlinear (composite) problems as special cases.

Efficiency and Duality in Nondifferentiable Multiobjective Programming Involving Directional Derivative

“…x f x Following Jeyakumar and Mond [24], Kaul et al [8] and Slimani and Radjef [20], we give the following definitions. , : , :…”

Sufficiency and Duality in Nonsmooth Multiobjective Programming Problem under Generalized Univex Functions

“…Consequently, various generalizations of convex functions have been introduced in the literature (see Hanson [1], Vial [2], Hanson and Mond [3], Jeyakumar and Mond [4], Hanson et al [5], Liang et al [6], and Gulati et al [7]). …”

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

“…Motivated by various concepts of convexity, Liang et al [5] have put forward a generalized convexity, which was called ( , , , )-convex, which extended ( , )-convex, and Liang et al [6], Weir and Mond [7], Weir [8], Jeyakumar and Mond [9], Egudo [10], Preda [2], and Gulati and Islam [3] obtained some corresponding optimality conditions and applied these optimality conditions to define dual problems and derived duality theorems for single objective fractional problems and multiobjective problems. Then the definition of generalized ( , , , )-convex is given under the condition of ( , , , )-convex.…”