5 papers · 1 filter
Characterizations of Faces of Convex Sets in Infinite-dimensional Vector Spaces
Valentin V. Gorokhovik
In the paper three different characterizations of faces of convex sets, belonging to infinite-dimensional real vector spaces, are presented. The first one is formulated in the term…
Infinite-dimensional Convex Cones: Internal Geometric Structure and Analytical Representation
Valentin V. Gorokhovik
In the paper we consider convex cones in infinite-dimensional real vector spaces which are endowed with no topology. The main purpose is to study an internal geometric structure of…
Internal structure and analytical representation of preference relations defined on infinite-dimensional real vector spaces
V. V. Gorokhovik
The paper deals with partial and weak preference relations defined on infinite-dimensional vector spaces and compatible with algebraic operations. By a partial preference we mean a…
High order tangent vectors to sets with applications to constrained optimization problems
Valentin V. Gorokhovik
We introduce an extended tangent cone of high order to a set and study its properties. Then we use this local approximation for deriving high-order necessary conditions for local m…
Regularly abstract convex functions with respect to the set of Lipschitz continuous concave functions
Valentin V. Gorokhovik
The goal of the paper is to study the particular class of regularly -convex functions, when is the set of…