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<p>This paper investigates the notion of compact R-continuity and its specifications for set-valued mappings between Banach spaces. We establish several important properties of compact R-continuity in general settings and show that in finite dimensions, this notion is supported by the classical Łojasiewicz inequality for analytic functions. Applications of compact R-continuity and the results obtained herein are provided through the convergence analysis for a broad class of descent algorithms in nonsmooth optimization. Moreover, we demonstrate that compact R-continuity plays a key role in the design and theoretical justification of a novel R-class of algorithms for solving general inclusion problems.</p>

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Compact R-Continuity with Applications to Solving Inclusions and Convergence of Algorithms

  • 期刊论文

  • 发表日期：

    2026年4月8日

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  • Ba Khiet Le,
  • Boris S. Mordukhovich,
  • Michel A. Théra

摘要

This paper investigates the notion of compact R-continuity and its specifications for set-valued mappings between Banach spaces. We establish several important properties of compact R-continuity in general settings and show that in finite dimensions, this notion is supported by the classical Łojasiewicz inequality for analytic functions. Applications of compact R-continuity and the results obtained herein are provided through the convergence analysis for a broad class of descent algorithms in nonsmooth optimization. Moreover, we demonstrate that compact R-continuity plays a key role in the design and theoretical justification of a novel R-class of algorithms for solving general inclusion problems.