{"ID":2843842,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.06868","arxiv_id":"2511.06868","title":"On the diameter of subgradient sequences in o-minimal structures","abstract":"We study subgradient sequences of locally Lipschitz functions definable in a polynomially bounded o-minimal structure. We show that the diameter of any subgradient sequence is related to the variation in function values, with error terms dominated by a double summation of step sizes. Consequently, we prove that bounded subgradient sequences converge if the step sizes are of order $1/k$. The proof uses Lipschitz $L$-regular stratifications in o-minimal structures to analyze subgradient sequences via their projections onto different strata.","short_abstract":"We study subgradient sequences of locally Lipschitz functions definable in a polynomially bounded o-minimal structure. We show that the diameter of any subgradient sequence is related to the variation in function values, with error terms dominated by a double summation of step sizes. Consequently, we prove that bounded...","url_abs":"https://arxiv.org/abs/2511.06868","url_pdf":"https://arxiv.org/pdf/2511.06868v3","authors":"[\"Lexiao Lai\",\"Mingzhi Song\"]","published":"2025-11-10T09:11:07Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"math.DS\"]","methods":"[]","has_code":false}