The definition of generalized unified (C, α, ρ, d)-convex function is given. The concepts of generalized unified (C, α, ρ, d)-quasiconvexity, generalized unified (C, α, ρ, d)-pseudoconvexity and generalized unif...The definition of generalized unified (C, α, ρ, d)-convex function is given. The concepts of generalized unified (C, α, ρ, d)-quasiconvexity, generalized unified (C, α, ρ, d)-pseudoconvexity and generalized unified (C, α, ρ, d)-strictly pseudoconvex functions are presented. The sufficient optimality conditions for multiobjective nonsmooth semi-infinite programming are obtained involving these generalized convexity lastly.展开更多
This paper is concerned with the study of optimality conditions for minimax optimization problems with an infinite number of constraints,denoted by(MMOP).More precisely,we first establish necessary conditions for opti...This paper is concerned with the study of optimality conditions for minimax optimization problems with an infinite number of constraints,denoted by(MMOP).More precisely,we first establish necessary conditions for optimal solutions to the problem(MMOP)by means of employing some advanced tools of variational analysis and generalized differentiation.Then,sufficient conditions for the existence of such solutions to the problem(MMOP)are investigated with the help of generalized convexity functions defined in terms of the limiting subdifferential of locally Lipschitz functions.Finally,some of the obtained results are applied to formulating optimality conditions for weakly efficient solutions to a related multiobjective optimization problem with an infinite number of constraints,and a necessary optimality condition for a quasiε-solution to problem(MMOP).展开更多
基金Supported by the Science Foundation of Shaanxi Provincial Educational Department Natural Science Foundation of China（06JK152） Supported by the Graduate Innovation Project of Yanan uni- versity（YCX201003）
文摘The definition of generalized unified (C, α, ρ, d)-convex function is given. The concepts of generalized unified (C, α, ρ, d)-quasiconvexity, generalized unified (C, α, ρ, d)-pseudoconvexity and generalized unified (C, α, ρ, d)-strictly pseudoconvex functions are presented. The sufficient optimality conditions for multiobjective nonsmooth semi-infinite programming are obtained involving these generalized convexity lastly.
基金supported by the National Natural Science Foundation of China(No.11761072)the Project of Jilin Science and Technology Development for Leading Talent of Science and Technology Innovation in Middle and Young and Team Project(No.20200301053RQ)。
文摘This paper is concerned with the study of optimality conditions for minimax optimization problems with an infinite number of constraints,denoted by(MMOP).More precisely,we first establish necessary conditions for optimal solutions to the problem(MMOP)by means of employing some advanced tools of variational analysis and generalized differentiation.Then,sufficient conditions for the existence of such solutions to the problem(MMOP)are investigated with the help of generalized convexity functions defined in terms of the limiting subdifferential of locally Lipschitz functions.Finally,some of the obtained results are applied to formulating optimality conditions for weakly efficient solutions to a related multiobjective optimization problem with an infinite number of constraints,and a necessary optimality condition for a quasiε-solution to problem(MMOP).
