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<p>This paper develops two parameter-free methods for solving convex and strongly convex hybrid composite universal problems, namely, a composite subgradient type method and a proximal bundle type method. Functional complexity bounds for the two methods are established in terms of the unknown strong convexity parameter. The two proposed methods are universal with respect to all problem parameters, including the strong convexity one, and require no knowledge of the optimal value. Moreover, in contrast to previous works, they do not restart nor use multiple threads.</p>

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Universal Subgradient and Proximal Bundle Methods for Convex and Strongly Convex Hybrid Composite Optimization

  • 期刊论文

  • 发表日期：

    2026年2月18日

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  • Vincent Guigues,
  • Jiaming Liang,
  • Renato D. C. Monteiro

摘要

This paper develops two parameter-free methods for solving convex and strongly convex hybrid composite universal problems, namely, a composite subgradient type method and a proximal bundle type method. Functional complexity bounds for the two methods are established in terms of the unknown strong convexity parameter. The two proposed methods are universal with respect to all problem parameters, including the strong convexity one, and require no knowledge of the optimal value. Moreover, in contrast to previous works, they do not restart nor use multiple threads.