4 citations · 4 across the 6 of their papers we have counts for
6 papers
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…
Minimal convex majorants of functions and Demyanov--Rubinov super(sub)differentials
Valentin V. Gorokhovik
The primary goal of the paper is to establish characteristic properties of (extended) real-valued functions defined on normed vector spaces that admit the representation as the low…
Saddle representations of positively homogeneous functions by linear functions
Valentin V. Gorokhovik, Marina Trafimovich
We say that a positively homogeneous function admits a saddle representation by linear functions iff it admits both an inf-sup-representation and a sup-inf-representation with the…
On extension of partial orders to total preorders with prescribed symmetric part
Dmitry V. Akopian, Valentin V. Gorokhovik
For a partial order on a set X and an equivalency relation S defined on the same set X we derive a necessary and sufficient condition for the existence of such a total pr…
Geometrical and analytical characteristic properties of piecewise affine mappings
V. V. Gorokhovik
Let X and Y be finite dimensional normed spaces, F(X,Y) a collection of all mappings from X into Y. A mapping is said to be piecewise affine if there exists a finite…