Scholarlink

<p>This paper addresses the zero-point problem of pseudomonotone vector fields with convex constraints on Hadamard manifolds. We propose a new derivative-free projection method by refining the separating-set projection technique and incorporating inertial extrapolation technique. The global convergence of this new method is established under the assumptions that the constructed separating sets are closed and convex, the vector field is continuous, and the solution set is nonempty. By assuming Lipschitz continuity and a local error bound condition, we demonstrate a local linear convergence rate on Hadamard manifolds with curvature bounded from below. Standard numerical experiments and applications, such as computing the Riemannian <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11075_2025_2254_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(L^2\)</EquationSource> </InlineEquation> center of mass, demonstrate the algorithm’s effectiveness.</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

Convergence properties of a new projection algorithm for pseudomonotone vector fields on hadamard manifolds

  • 期刊论文

  • 发表日期：

    2025年10月31日

查看全文
  • Teng-Teng Yao,
  • Yong-Yan Yue,
  • Zhi Zhao

摘要

This paper addresses the zero-point problem of pseudomonotone vector fields with convex constraints on Hadamard manifolds. We propose a new derivative-free projection method by refining the separating-set projection technique and incorporating inertial extrapolation technique. The global convergence of this new method is established under the assumptions that the constructed separating sets are closed and convex, the vector field is continuous, and the solution set is nonempty. By assuming Lipschitz continuity and a local error bound condition, we demonstrate a local linear convergence rate on Hadamard manifolds with curvature bounded from below. Standard numerical experiments and applications, such as computing the Riemannian \(L^2\) center of mass, demonstrate the algorithm’s effectiveness.