Scholarlink

<p>In this paper we introduce the Boosted Double-proximal Subgradient Algorithm (BDSA), a novel splitting algorithm designed to address general structured nonsmooth and nonconvex mathematical programs expressed as sums and differences of composite functions. BDSA exploits the combined nature of subgradients from the data and proximal steps, and integrates a linesearch procedure to enhance its performance. While BDSA encompasses existing schemes proposed in the literature, it extends its applicability to more diverse problem domains. We establish the convergence of BDSA under the Kurdyka–Łojasiewicz property and provide an analysis of its convergence rate. To evaluate the effectiveness of BDSA, we introduce two novel test functions with an abundance of critical points. We conduct comparative evaluations, including algorithms with inertial terms, that illustrate its ability to effectively escape non-optimal critical points. Additionally, we present two practical applications of BDSA for testing its efficacy, namely, a constrained minimum-sum-of-squares clustering problem and a nonconvex generalization of Heron’s problem.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

The Boosted Double-proximal Subgradient Algorithm for nonconvex optimization

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年2月25日

查看全文
  • Francisco J. Aragón-Artacho,
  • Pedro Pérez-Aros,
  • David Torregrosa-Belén

摘要

In this paper we introduce the Boosted Double-proximal Subgradient Algorithm (BDSA), a novel splitting algorithm designed to address general structured nonsmooth and nonconvex mathematical programs expressed as sums and differences of composite functions. BDSA exploits the combined nature of subgradients from the data and proximal steps, and integrates a linesearch procedure to enhance its performance. While BDSA encompasses existing schemes proposed in the literature, it extends its applicability to more diverse problem domains. We establish the convergence of BDSA under the Kurdyka–Łojasiewicz property and provide an analysis of its convergence rate. To evaluate the effectiveness of BDSA, we introduce two novel test functions with an abundance of critical points. We conduct comparative evaluations, including algorithms with inertial terms, that illustrate its ability to effectively escape non-optimal critical points. Additionally, we present two practical applications of BDSA for testing its efficacy, namely, a constrained minimum-sum-of-squares clustering problem and a nonconvex generalization of Heron’s problem.