The theory of increasing and convex-along-rays(ICAR)functions defined on a convex cone in a real locally convex topological vector space X was already well developed.In this paper,we first examine abstract convexity o...The theory of increasing and convex-along-rays(ICAR)functions defined on a convex cone in a real locally convex topological vector space X was already well developed.In this paper,we first examine abstract convexity of increasing plus-convex-along-rays(IPCAR)functions defined on a real normed linear space X.We also study,for this class of functions,some concepts of abstract convexity,such as support sets and subdifferentials.Finally,as an application,we characterize the maximal elements of the support set of strictly IPCAR functions and give optimality conditions for the global minimum of the difference between two IPCAR functions.展开更多
基金the Mahani Mathematical Research Center,Iran,grant no:97/3267。
文摘The theory of increasing and convex-along-rays(ICAR)functions defined on a convex cone in a real locally convex topological vector space X was already well developed.In this paper,we first examine abstract convexity of increasing plus-convex-along-rays(IPCAR)functions defined on a real normed linear space X.We also study,for this class of functions,some concepts of abstract convexity,such as support sets and subdifferentials.Finally,as an application,we characterize the maximal elements of the support set of strictly IPCAR functions and give optimality conditions for the global minimum of the difference between two IPCAR functions.
