On Integrated Convex Optimization in Normed Linear Space
نویسندگان
چکیده
Abstract In this paper, the concept of generalized saddle point(GSP) is employed to discuss the optimization problems of a set of convex functions on a normed linear space X , which presents an equivalence under a special condition between GSP and its optimum solution. A study on integrated convex optimization problem by using Gâteaux and Fréchet differentiability respectivly, and the equivalent relationships among GSP, Gâteaux and Fréchet differentiability respectively, and optimum solution are concerned in this paper.
منابع مشابه
GRADUAL NORMED LINEAR SPACE
In this paper, the gradual real numbers are considered and the notion of the gradual normed linear space is given. Also some topological properties of such spaces are studied, and it is shown that the gradual normed linear space is a locally convex space, in classical sense. So the results in locally convex spaces can be translated in gradual normed linear spaces. Finally, we give an examp...
متن کاملFuzzy Topology Generated by Fuzzy Norm
In the current paper, consider the fuzzy normed linear space $(X,N)$ which is defined by Bag and Samanta. First, we construct a new fuzzy topology on this space and show that these spaces are Hausdorff locally convex fuzzy topological vector space. Some necessary and sufficient conditions are established to illustrate that the presented fuzzy topology is equivalent to two previously studied fuz...
متن کاملFunctionally closed sets and functionally convex sets in real Banach spaces
Let $X$ be a real normed space, then $C(subseteq X)$ is functionally convex (briefly, $F$-convex), if $T(C)subseteq Bbb R $ is convex for all bounded linear transformations $Tin B(X,R)$; and $K(subseteq X)$ is functionally closed (briefly, $F$-closed), if $T(K)subseteq Bbb R $ is closed for all bounded linear transformations $Tin B(X,R)$. We improve the Krein-Milman theorem ...
متن کاملExistence Results of best Proximity Pairs for a Certain Class of Noncyclic Mappings in Nonreflexive Banach Spaces Polynomials
Introduction Let be a nonempty subset of a normed linear space . A self-mapping is said to be nonexpansive provided that for all . In 1965, Browder showed that every nonexpansive self-mapping defined on a nonempty, bounded, closed and convex subset of a uniformly convex Banach space , has a fixed point. In the same year, Kirk generalized this existence result by using a geometric notion of ...
متن کاملThe SECQ, Linear Regularity, and the Strong CHIP for an Infinite System of Closed Convex Sets in Normed Linear Spaces
We consider a (finite or infinite) family of closed convex sets with nonempty intersection in a normed space. A property relating their epigraphs with their intersection’s epigraph is studied, and its relations to other constraint qualifications (such as the linear regularity, the strong CHIP, and Jameson’s (G)-property) are established. With suitable continuity assumption we show how this prop...
متن کامل