Abstract:This paper deals with nonsmooth convex optimization problems in Euclidean spaces. We identify special elements of the subdifferential of a convex function, called specular gradients. Based on this observation, we propose three numerical methods that use specular gradients in subgradient methods. We prove the convergence of the proposed methods under suitable step sizes. Numerical experiments demonstrate that the proposed methods are capable of minimizing non-differentiable functions that classical methods fail to minimize.
| Comments: | 19 pages. This paper is part of a split of the previous preprint arXiv:2601.10950, and addresses numerical applications |
| Subjects: | Optimization and Control (math.OC); Numerical Analysis (math.NA) |
| MSC classes: | 49J52, 65K10, 90C25, 90C15 |
| Cite as: | arXiv:2605.25490 [math.OC] |
| (or arXiv:2605.25490v1 [math.OC] for this version) | |
| https://doi.org/10.48550/arXiv.2605.25490 arXiv-issued DOI via DataCite (pending registration) |
From: Kiyuob Jung [view email]
[v1]
Mon, 25 May 2026 06:51:11 UTC (1,679 KB)
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