{"ID":2875222,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.01872","arxiv_id":"2509.01872","title":"Compact R-Continuity with Applications to Solving Inclusions and Convergence of Algorithms","abstract":"This paper investigates the notion of compact R-continuity and its specifications for set-valued mappings between Banach spaces. We reveal several important properties of compact R-continuity in general settings and show that in finite dimensions, this notion is supported by the classical Lojasiewicz inequality for analytic functions. An application of compact R-continuity and the obtained results is given to convergence analysis for a broad class of descent algorithms in nonsmooth optimization. We also show that this notion is instrumental for the design and justification of a novel R-class of algorithms to solve inclusion problems.","short_abstract":"This paper investigates the notion of compact R-continuity and its specifications for set-valued mappings between Banach spaces. We reveal several important properties of compact R-continuity in general settings and show that in finite dimensions, this notion is supported by the classical Lojasiewicz inequality for ana...","url_abs":"https://arxiv.org/abs/2509.01872","url_pdf":"https://arxiv.org/pdf/2509.01872v2","authors":"[\"Ba Khiet Le\",\"Boris S. Mordukhovich\",\"Michel A. Thera\"]","published":"2025-09-02T01:34:26Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}