Optimality Conditions And Duality For E-Differentiable Interval Valued Optimization Problems With Generalized Convexity

This paper is devoted to the study of optimality conditions and duality of interval-valued programming problems,including optimality and duality of Epreinvex interval valued programming,optimality and duality of E-invex fractional multi-objective interval valued programming,and Fritz-John type optimality conditions of E-quasi convex gH-symmetric differentiable interval valued programming problem.The details are as follows.1.E-KKT optimality conditions for E-preinvex interval valued programming problemThe generalized convexity of interval valued functions is generalized in the Edifferentiable case and the properties between these generalized convexities are discussed.In addition,the optimality conditions of the interval valued programming problem are mainly studied under the E-preinvex E-differentiable assumption,and the necessary and su cient conditions for E-KKT optimality are obtained,and the correctness of the results is verified by examples.2.Optimality conditions and duality of the E-invariant convex E-differentiable multi-objective interval-valued programming problemThe E-invexity of fractional interval-valued functions and fractional interval valued vector functions is given in the E-differentiable case,and the existence of such generalized convex fractional interval valued functions is verified by examples.Moreover,the optimality conditions of fractional multi-objective interval valued programming are investigated under the assumptions of E-invexity and E-differentiability.In addition,the solution of the invariant convex fractional interval programming problem is also inscribed,while the Mond-Weir weak duality and strong duality of the E-invex fractional multi-objective interval-valued programming are studied under appropriate conditions.3.Fritz-John type optimality conditions for the gH-symmetric differentiable interval valued programming problemUnder the assumption of gH-symmetric differentiability,the definitions of Equasi convexity and E-pseudo convexity of interval-valued functions are given,and the relationships of these generalized convex interval valued functions are discussed.In addition,Fritz-John optimality conditions for interval valued programming problem are given under the assumptions of E-pseudo-convexity,E-quasi-convexity,and gH-symmetric differentiability.