Registration Number
0225U000461,
(0124U002162)
, R & D reports
Title
New Subgradient and Extragradient Methods for Non-smooth Regression Problems
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Розробка субградієнтних та екстраградієнтних алгоритмів для задач регресії з гьольдеровими нормами та задач непараметричної регресії
Head
Liashko Serhii I., д.ф.-м.н.
Serhiienko Ivan V., Доктор фізико-математичних наук
Registration Date
12-01-2025
Organization
Department for special training National academy of science of Ukraine at Kiev University
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The goal of scientific research is to create new effective subgradient and extragradient methods with theoretical justification for non-smooth regression problems.
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The main problem statements and subgradient and extragradient methods are analyzed, in particular, an -algorithm with an adaptive step adjustment method and a variant of the non-smooth penalty function method are described; a parametric version of the ellipsoid method for convex programming problems and convex-concave saddle problems are described; direct-dual smooth and non-smooth statements of regression-type problems with Hölder norms are formulated, for which new extragradient algorithms are proposed; various variants of the non-parametric convex regression problem statement are formulated.
The application of the emshor ellipsoid method algorithm to solve the Sylvester problem of the smallest limiting hypersphere and its generalization to the case of a finite set of -dimensional balls given by their centers and radii are investigated. Based on the emshor method, the algorithms sylvester1 for solving the problem of minimizing a convex piecewise quadratic function, which is equivalent to the problem of finding a sphere of minimal radius for a finite set of points, and sylvester2 for minimizing a convex function, which is equivalent to the generalized problem of finding a sphere of minimal radius for a finite set of spheres with their given centers and radii, were built.
Variational inequalities with monotone operators acting in Hilbert space are considered, and two methods of their approximate solution are considered – the algorithm of extrapolation from the past and the algorithm of operator extrapolation, for which convergence theorems and non-asymptotic estimates of the linear rate of convergence are proved. A new decentralized distributed algorithm is constructed for the problem of finding the saddle point of the sum of convex-concave functions.
Product Description
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Kovalenko Oleksandra Yu.
Korablov Mykola M.
Volodymyr V. Semenov
Stetsiuk Petro I.
Stovba Viktor O.
Cherhykalo Denys O.
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2025-01-12
