Abstract
On the basis of arcwise connected convex functions and (p, r) −η - invex functions, we established Hb –(p, r) –η- invex functions. Based on the generalized invex assumption of new functions, the solutions of a class of multiobjective fractional programming problems are studied, and the sufficient optimality condition for the feasible solutions of multiobjective fractional programming problems to be efficient solutions are established and proved.
Highlights
Multiobjective programming is a branch of mathematical programming
Multiobjective programming is widely used in many practical problems, such as economy, management, military affairs, science and engineering design
In view of its importance in mathematical programming theory and application, many researches are devoted to popularizing these concepts to expand their application scope.M.A.Hanson studied the sufficiency of the Kuhn-Tucker[1];Avriel M and Zang I put forward a new class of generalized convex functions, and on this basis, gives some regularity conditions satisfying the characteristics of local-global minimum[2]; In reference[3], a new class of generalized convex functions is defined by means of symmetric gradient.In reference[4,5], the optimality conditions and Wolfe-type duality of two classes of invariant convex multiobjective nonlinear programming are proposed
Summary
Multiobjective programming is a branch of mathematical programming. The idea of multiobjective optimization was first put forward by French economist V. pareto in 1896. In view of its importance in mathematical programming theory and application, many researches are devoted to popularizing these concepts to expand their application scope.M.A.Hanson studied the sufficiency of the Kuhn-Tucker[1];Avriel M and Zang I put forward a new class of generalized convex functions, and on this basis, gives some regularity conditions satisfying the characteristics of local-global minimum[2]; In reference[3], a new class of generalized convex functions is defined by means of symmetric gradient.In reference[4,5], the optimality conditions and Wolfe-type duality of two classes of invariant convex multiobjective nonlinear programming are proposed. Based on the generalized invariant convex assumption of new functions, the solutions of a class of multiobjective fractional programming problems are studied, and some optimality.
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