arXiv subjects

I. M. Prudnikov

Publications and source records attributed to I. M. Prudnikov.

2 recordsLinked to original sources

arXiv2026

Upper and lower approximations of the second order. Exhausters of the second order

The upper and lower approximations of the second order are defined for a function differentiable in the directions. Exhausters of the second order are introduced. The relation between the second-order Frechet subdifferentials and the second-order exhausters is given. A rule for constructing exhausters of the first and second orders is given for Lipschitz functions.Necessary and sufficient extremum conditions through exhausters are given. It is discussed about the use of Exhausters in optimization.

math.OC↗

arXiv2023

Accelerated method of finding for the minimum of arbitrary Lipschitz convex function

The goal of the paper is development of an optimization method with the superlinear convergence rate for a nonsmooth convex function. For optimization an approximation is used that is similar to the Steklov integral averaging. The difference is that averaging is performed over a variable-dependent set, that is called a set-valued mapping (SVM) satisfying simple conditions. Novelty approach is that with such an approximation we obtain twice continuously differentiable convex functions, for optimizations of which are applied methods of the second order. The estimation of the convergence rate of the method is given.

math.OC↗