Continuous Convex Sets.
نویسندگان
چکیده
منابع مشابه
Continuous Convex Sets and Zero Duality Gap for Convex Programs
This article uses classical notions of convex analysis over euclidean spaces, like Gale & Klee’s boundary rays and asymptotes of a convex set, or the inner aperture directions defined by Larman and Brøndsted for the same class of sets, to provide a new zero duality gap criterion for ordinary convex programs. On this ground, we are able to characterize objective functions and respectively feasib...
متن کاملContinuous rotation invariant valuations on convex sets
The notion of valuation on convex sets can be considered as a generalization of the notion of measure, which is defined only on the class of convex compact sets. It is well-known that there are important and interesting examples of valuations on convex sets, which are not measures in the usual sense as, for example, the mixed volumes. Basic definitions and some classical examples are discussed ...
متن کاملConvex Sets and Convex Combinations
Convexity is one of the most important concepts in a study of analysis. Especially, it has been applied around the optimization problem widely. Our purpose is to define the concept of convexity of a set on Mizar, and to develop the generalities of convex analysis. The construction of this article is as follows: Convexity of the set is defined in the section 1. The section 2 gives the definition...
متن کاملConvex Sets and Convex Functions
In this section, we introduce one of the most important ideas in economic modelling, in the theory of optimization and, indeed in much of modern analysis and computatyional mathematics: that of a convex set. Almost every situation we will meet will depend on this geometric idea. As an independent idea, the notion of convexity appeared at the end of the 19 century, particularly in the works of M...
متن کاملConvex Sets
Javier Alonso*, Pedro Mart́ın. Universidad de Extremadura, Badajoz, Spain. Characterizations of ellipsoids by sections. Let S be the boundary of a convex body in the d-dimensional Euclidean space E (d ≥ 3). It is well known that S is an ellipsoid if and only if the section of S given by any hyperplane is ellipsoidal. The question of whether it is actually necessary to consider “any” hyperplane t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: MATHEMATICA SCANDINAVICA
سال: 1959
ISSN: 1903-1807,0025-5521
DOI: 10.7146/math.scand.a-10585