{"ID":2830625,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.09439","arxiv_id":"2512.09439","title":"Parameter-Free Accelerated Quasi-Newton Method for Nonconvex Optimization","abstract":"We propose a quasi-Newton-type method for nonconvex optimization with Lipschitz continuous gradients and Hessians. The algorithm finds an $\\varepsilon$-stationary point within $\\tilde{\\mathrm{O}}(d^{1/4} \\varepsilon^{-13/8})$ gradient evaluations, where $d$ is the problem dimension. Although this bound includes an additional logarithmic factor compared with the best known complexity, our method is parameter-free in the sense that it requires no prior knowledge of problem-dependent parameters such as Lipschitz constants or the optimal value. Moreover, it does not need the target accuracy $\\varepsilon$ or the total number of iterations to be specified in advance. The result is achieved by combining several key ideas: momentum-based acceleration, quartic regularization for subproblems, and a scaled variant of the Powell-symmetric-Broyden (PSB) update.","short_abstract":"We propose a quasi-Newton-type method for nonconvex optimization with Lipschitz continuous gradients and Hessians. The algorithm finds an $\\varepsilon$-stationary point within $\\tilde{\\mathrm{O}}(d^{1/4} \\varepsilon^{-13/8})$ gradient evaluations, where $d$ is the problem dimension. Although this bound includes an addi...","url_abs":"https://arxiv.org/abs/2512.09439","url_pdf":"https://arxiv.org/pdf/2512.09439v1","authors":"[\"Naoki Marumo\"]","published":"2025-12-10T09:08:25Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}