{"ID":2883483,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.07535","arxiv_id":"2508.07535","title":"Randomized coordinate gradient descent almost surely escapes strict saddle points","abstract":"We analyze the behavior of randomized coordinate gradient descent for nonconvex optimization, proving that under standard assumptions, the iterates almost surely escape strict saddle points. By formulating the method as a nonlinear random dynamical system and characterizing neighborhoods of critical points, we establish this result through the center-stable manifold theorem.","short_abstract":"We analyze the behavior of randomized coordinate gradient descent for nonconvex optimization, proving that under standard assumptions, the iterates almost surely escape strict saddle points. By formulating the method as a nonlinear random dynamical system and characterizing neighborhoods of critical points, we establis...","url_abs":"https://arxiv.org/abs/2508.07535","url_pdf":"https://arxiv.org/pdf/2508.07535v1","authors":"[\"Ziang Chen\",\"Yingzhou Li\",\"Zihao Li\"]","published":"2025-08-11T01:31:19Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"math.DS\",\"math.NA\",\"math.PR\"]","methods":"[]","has_code":false}