采用Polyak步长的随机迭代方法求解广义绝对值方程
Randomized iterative methods with Polyak step-size for solving generalized absolute value equations
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中文总结 AI 辅助
本文将Polyak步长融入随机迭代方法，针对动态更新目标函数的场景完成收敛分析，证实其期望线性收敛性，实验显示该方法可大幅提升随机迭代方法的计算性能。
中文摘要 AI 辅助
本文将Polyak步长系统地融入随机迭代方法，以提升其求解广义绝对值方程的效率。具体而言，我们在随机迭代框架内采用Polyak步长，该框架下目标函数每一步都会动态更新，不同于专为固定目标函数的确定性优化设计的经典Polyak步长。因此，这种新实现方式与传统Polyak方案不同，需要专门的收敛性分析。我们严格分析了所提方法的收敛特性，确立了其期望意义下的线性收敛性。数值实验表明，引入Polyak步长能显著提升采用固定步长的随机迭代方法的计算性能。
英文摘要
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.
