Sequential Subspace Optimization for Quasar-Convex Optimization Problems with Inexact Gradient

• Published in: Advances in Optimization and Applications Vol. 1514; pp. 19 - 33
• Main Authors: Kuruzov, Ilya A., Stonyakin, Fedor S.
• Format: Book Chapter
• Language: English
• Published: Switzerland Springer International Publishing AG 2021; Springer International Publishing
• Series: Communications in Computer and Information Science
• Subjects: Inexact gradient; Quasar-convex functions; Subspace optimization method
• ISBN: 9783030927103; 3030927105
• ISSN: 1865-0929; 1865-0937
• DOI: 10.1007/978-3-030-92711-0_2

It is well-known that accelerated first-order 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 gradient information. However, this can lead to an accumulation of corresponding inexactness in the theoretical estimates of the rate of convergence. We propose one modification of the Sequential Subspace Optimization Method (SESOP) for minimization problems with γ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma $$\end{document}-quasar-convex functions with inexact gradient. A theoretical result is obtained indicating the absence of accumulation of gradient inexactness. A numerical implementation of the proposed version of the SESOP method and its comparison with the known Similar Triangle Method with an inexact gradient is carried out.