1. Главная
  2. Ресурсы
  3. Библиотечный поиск
Gradient Method withStep Adaptation :научное издание Krutikov VladimirTovbis ElenaGutova Svetlana2025 год

Gradient Method with Step Adaptation : научное издание
статья из журнала

Дополнительные ссылки: eLibrary
База данных: Каталог библиотеки СФУ
Библиографическое описание: Gradient Method with Step Adaptation : научное издание / V. V. Krutikov [et al.]. - Текст : непосредственный // Mathematics. - 2025. - Т. 13, № 1. - P. 61. - This research was funded by the Ministry of Science and Higher Education of the Russian Federation, project no. FEFE-2023-0004. - ISSN 2227-7390, DOI 10.3390/math13010061.
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. Such methods 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>
Год издания: 2025
Авторы: Krutikov Vladimir , Tovbis Elena , Gutova Svetlana , Rozhnov Ivan , Kazakovtsev Lev
Издательство: MDPI, Basel
Источник: Mathematics
Выпуск: Т. 13, № 1
Номера страниц: 61
Держатель оригинала документа: Kemerovo State University, Reshetnev Siberian State University of Science and Technology, , Siberian Federal University
Количество экземпляров:
Твёрдая копия издания отсутствует в фонде библиотеки

Похожие публикации

Adam Algorithm withStep Adaptation Krutikov VladimirTovbis ElenaKazakovtsev Lev2025 год

Adam Algorithm with Step Adaptation : научное издание

  • Krutikov Vladimir и др.
  • 2025 год
Newtonian Property ofSubgradient Methodwith Optimization ofMetric MatrixParameter Correction Tovbis ElenaKrutikov VladimirKazakovtsev Lev2024 год

Newtonian Property of Subgradient Method with Optimization of Metric Matrix Parameter Correction : научное издание

  • Tovbis Elena и др.
  • 2024 год
On the ConvergenceRate of Quasi-NewtonMethods onStronglyConvex Functions withLipschitz Gradient Krutikov VladimirTovbis ElenaStanimirović Predrag2023 год

On the Convergence Rate of Quasi-Newton Methods onStrongly Convex Functions with Lipschitz Gradient : научное издание

  • Krutikov Vladimir и др.
  • 2023 год
A Family ofMulti-StepSubgradientMinimization Methods Tovbis ElenaKrutikov VladimirStanimirović Predrag2023 год

A Family of Multi-Step Subgradient Minimization Methods : научное издание

  • Tovbis Elena и др.
  • 2023 год
RelaxationSubgradientAlgorithms withMachine LearningProcedures Krutikov VladimirGutova SvetlanaTovbis Elena2022 год

Relaxation Subgradient Algorithms with Machine Learning Procedures : научное издание

  • Krutikov Vladimir и др.
  • 2022 год
Algorithm for ScalingVariables inMinimization Methods Tovbis ElenaKrutikov VladimirKazakovtsev Lev2026 год

Algorithm for Scaling Variables in Minimization Methods : научное издание

  • Tovbis Elena и др.
  • 2026 год
Fuzzy AdaptiveParameter in theDai–Liao OptimizationMethod Based onNeutrosophy Stanimirović Predrag S.Ivanov Branislav D.Stanujkić Dragiša2023 год

Fuzzy Adaptive Parameter in the Dai–Liao Optimization Method Based on Neutrosophy : научное издание

  • Stanimirović Predrag S. и др.
  • 2023 год
Properties andApplication ofIncompleteOrthogonalization inthe Directions ofGradient Differencein Optimization… Krutikov VladimirTovbis ElenaGutova Svetlana2025 год

Properties and Application of Incomplete Orthogonalization in the Directions of Gradient Difference… : научное издание

  • Krutikov Vladimir и др.
  • 2025 год

Показать ещё

Improved gradientprojection method forparametricoptimisation of barstructures Yurchenko V. V.Peleshko I. D.2020 год

Improved gradient projection method for parametric optimisation of bar structures : статья из журнала

  • Yurchenko V. V. и др.
  • 2020 год
HeuristicGreedy-Gradient RouteSearch Method forFinding an OptimalTraffic Distributionin TelecommunicationNetworks Gaipov KonstantinTausnev DaniilKhodenkov Sergey2024 год

Heuristic Greedy-Gradient Route Search Method for Finding an Optimal Traffic Distribution in… : научное издание

  • Gaipov Konstantin и др.
  • 2024 год
A Modified Dai-LiaoConjugate GradientMethod Based on aScalar MatrixApproximation ofHessian and ItsApplication Ivanov BranislavMilovanović Gradimir V.Stanimirović Predrag S.2023 год

A Modified Dai-Liao Conjugate Gradient Method Based on a Scalar Matrix Approximation of Hessian and… : научное издание

  • Ivanov Branislav и др.
  • 2023 год
A ConservativeSemi-LagrangianMethod for aContinuity Equationwith Various TimeSteps in DifferentParts of the… Vyatkin A. V.Maltsev A. D.2024 год

A Conservative Semi-Lagrangian Method for a Continuity Equation with Various Time Steps in… : статья из журнала

  • Vyatkin A. V. и др.
  • 2024 год
Machine Learning inQuasi-Newton Methods Krutikov VladimirTovbis ElenaStanimirović Predrag2024 год

Machine Learning in Quasi-Newton Methods : научное издание

  • Krutikov Vladimir и др.
  • 2024 год
Hyper-HeuristicApproach for TuningParameter Adaptationin DifferentialEvolution Stanovov VladimirKazakovtsev LevSemenkin Eugene2024 год

Hyper-Heuristic Approach for Tuning Parameter Adaptation in Differential Evolution : научное издание

  • Stanovov Vladimir и др.
  • 2024 год
A Method forTransformingNon-ConvexOptimization Problemto Distributed Form Khamisov Oleg O.Khamisov Oleg V.Ganchev Todor D.2024 год

A Method for Transforming Non-Convex Optimization Problem to Distributed Form : статья из журнала

  • Khamisov Oleg O. и др.
  • 2024 год
Improved GradientDescent Iterationsfor Solving Systemsof NonlinearEquations Stanimirović Predrag S.Shaini Bilall I.Sabi’u Jamilu2023 год

Improved Gradient Descent Iterations for Solving Systems of Nonlinear Equations : научное издание

  • Stanimirović Predrag S. и др.
  • 2023 год