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<p>This study presents an advanced two-step inertial proximal coordinate algorithm (TIPSCA) designed to minimize the sum of multiple separable nonconvex and potentially nonsmooth objective functions along with a single smooth, nonseparable function that may also be nonconvex. The proposed method, termed the two-step inertial proximal coordinate subgradient algorithm, iteratively refines the solution by applying the proximal subgradients of the separable functions at the current solution point. The algorithm’s global convergence is established under the framework of the Kurdyka–Łojasiewicz (KŁ) property and several reasonable auxiliary conditions. The convergence rate is determined based on the Łojasiewicz exponent, providing a theoretical foundation for the algorithm’s performance. To demonstrate the practical applicability and efficiency of the proposed method, two numerical experiments are conducted, showcasing its capabilities in handling complex optimization problems.</p>

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Two-Step Inertial Proximal Coordinate Algorithms for Solving a Class of Nonsmooth and Nonconvex Optimization Problems

  • 期刊论文

  • 发表日期：

    2026年7月1日

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  • Ya-Lin Zhang,
  • Ya-Zheng Dang

摘要

This study presents an advanced two-step inertial proximal coordinate algorithm (TIPSCA) designed to minimize the sum of multiple separable nonconvex and potentially nonsmooth objective functions along with a single smooth, nonseparable function that may also be nonconvex. The proposed method, termed the two-step inertial proximal coordinate subgradient algorithm, iteratively refines the solution by applying the proximal subgradients of the separable functions at the current solution point. The algorithm’s global convergence is established under the framework of the Kurdyka–Łojasiewicz (KŁ) property and several reasonable auxiliary conditions. The convergence rate is determined based on the Łojasiewicz exponent, providing a theoretical foundation for the algorithm’s performance. To demonstrate the practical applicability and efficiency of the proposed method, two numerical experiments are conducted, showcasing its capabilities in handling complex optimization problems.