On Some Versions of Subspace Optimization Methods with Inexact Gradient Information

Ilya Kuruzov; Fedor Stonyakin

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arXiv · 2407.01051

On Some Versions of Subspace Optimization Methods with Inexact Gradient Information

Ilya Kuruzov·Fedor Stonyakin

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Abstract

It is well-known that accelerated gradient methods possess optimal complexity estimates for the class of convex smooth minimization problems. In many practical situations, it makes sense to work with inexact gradients. However, this can lead to the accumulation of corresponding inexactness in the theoretical estimates of the rate of convergence. We propose some modifications of first-order methods for convex optimization with an inexact gradient based on subspace optimization, such as Nemirovski's Conjugate Gradient method and the Sequential Subspace Optimization method. We study their convergence under different conditions on the inexactness both in the gradient value and in the accuracy of the solution of the subspace optimization subproblems. Besides this, we investigate a generalization of these results to the class of quasar-convex (weakly-quasi-convex) functions.

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BibTeX RIS

Ilya Kuruzov, Fedor Stonyakin. 2024-07-01. On Some Versions of Subspace Optimization Methods with Inexact Gradient Information. https://arxiv.org/abs/2407.01051

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