Compact R-Continuity with Applications to Solving Inclusions and Convergence of Algorithms
Optimization and Control
2025-09-05 v2
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.
Cite
@article{arxiv.2509.01872,
title = {Compact R-Continuity with Applications to Solving Inclusions and Convergence of Algorithms},
author = {Ba Khiet Le and Boris S. Mordukhovich and Michel A. Thera},
journal= {arXiv preprint arXiv:2509.01872},
year = {2025}
}