subdifferential

The External Estimate of the Compact Set by Lebesgue Set of the Convex Function

Authors: Abramova V. V., Dudov S. I., Osipcev M. A.

The finite-dimensional problem of embedding a given compact D ⊂ R p into the lower Lebesgue set G(α) = {y ∈ R p : f(y) 6 α} of the convex function f(·) with the smallest value of α due to the offset of D is considered. Its mathematical formalization leads to the problem of minimizing the function φ(x) = max y∈D f(y − x) on R p . The properties of the function φ(x) are researched, necessary and sufficient conditions and conditions for the uniqueness of the problem solution are obtained.

On a Approximate Solution of the Problem of Aspherical Convex Compact Set

Authors: Dudov S. I., Mesheryakova Е. А.

We examine a finite-dimensional problem of minimizing the ratio radius of the ball given a compact convex set (in an arbitrary norm) to the radius of the inscribed sphere through the choice of a common center of these balls. The article offers an approach to building the numerical method of its solution.

On Equivalence of the Method of Steepest Descent and the Method of Hypodifferential Descent in Some Constrained Optimization Problems

Authors: Dolgopolik M. V., Tamasyan G. S.

The method of exact penalty functions is widely used for the study of constrained optimization problems. The approach based on exact penalization was successfully applied to the study of optimal control problems and various problems of the calculus of variations, computational geometry and mathematical diagnostics. It is worth mentioning that even if the constrained optimization problem under consideration is smooth, the equivalent unconstrained optimization problems constructed via exact penalization technique is