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arXiv · 2608.00952

Randomized iterative methods with Polyak step-size for solving generalized absolute value equations

Jiayun Chen·Qiye Zhang·Deren Han·Jiaxin Xie
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Abstract

In this paper, we systematically incorporate the Polyak step-size into the randomized iterative method to improve its efficiency for solving generalized absolute value equations. In particular, we adopt the Polyak step-size within a stochastic iterative setting where the objective function updates dynamically at every step, unlike the classical Polyak step-size designed for deterministic optimization with fixed objective functions. Consequently, this novel implementation differs from the conventional Polyak scheme and demands a dedicated convergence analysis. We rigorously analyze the convergence properties of the proposed method and establish its linear convergence in expectation. Numerical experiments demonstrate that the incorporation of the Polyak step-size substantially improves the computational performance of randomized iterative methods with constant step-sizes.

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Jiayun Chen, Qiye Zhang, Deren Han, Jiaxin Xie. 2026-08-02. Randomized iterative methods with Polyak step-size for solving generalized absolute value equations. https://arxiv.org/abs/2608.00952

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