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

TL;DR

This paper introduces a modified SESOP method for quasar-convex optimization with inexact gradients, ensuring convergence without error accumulation, supported by theoretical analysis and numerical comparisons.

Contribution

It proposes a novel SESOP variant for quasar-convex problems with inexact gradients that avoids error accumulation, enhancing optimization robustness.

Findings

The modified SESOP method converges without inexactness accumulation.

Numerical experiments show competitive performance with the Similar Triangle Method.

Theoretical analysis confirms the method's stability against gradient inaccuracy.

Abstract

It is well-known that accelerated gradient first-order 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 some modification of the Sequential Subspace Optimization Method (SESOP) for minimization problems with 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.