Gradient Method with Step Adaptation : научное издание

Описание

Тип публикации: статья из журнала

Год издания: 2025

Идентификатор DOI: 10.3390/math13010061

Ключевые слова: minimization method, relaxation, gradient method, step adaptation, convergence rate

Аннотация: <jats:p>The paper solves the problem of constructing step adjustment algorithms for a gradient method based on the principle of the steepest descent. The expansion of the step adjustment principle, its formalization and parameterization led the researchers to gradient-type methods with incomplete relaxation or over-relaxation. SuchПоказать полностьюmethods require only the gradient of the function to be calculated at the iteration. Optimization of the parameters of the step adaptation algorithms enables us to obtain methods that significantly exceed the steepest descent method in terms of convergence rate. In this paper, we present a universal step adjustment algorithm that does not require selecting optimal parameters. The algorithm is based on orthogonality of successive gradients and replacing complete relaxation with some degree of incomplete relaxation or over-relaxation. Its convergence rate corresponds to algorithms with optimization of the step adaptation algorithm parameters. In our experiments, on average, the proposed algorithm outperforms the steepest descent method by 2.7 times in the number of iterations. The advantage of the proposed methods is their operability under interference conditions. Our paper presents examples of solving test problems in which the interference values are uniformly distributed vectors in a ball with a radius 8 times greater than the gradient norm.</jats:p>

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Издание

Журнал: Mathematics

Выпуск журнала: Т. 13, 1

Номера страниц: 61

ISSN журнала: 22277390

Место издания: Basel

Издатель: MDPI

Персоны

  • Krutikov Vladimir (Kemerovo State University)
  • Tovbis Elena (Reshetnev Siberian State University of Science and Technology, )
  • Gutova Svetlana (Kemerovo State University)
  • Rozhnov Ivan (Siberian Federal University)
  • Kazakovtsev Lev (Reshetnev Siberian State University of Science and Technology, )

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