{"ID":2852679,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.17366","arxiv_id":"2510.17366","title":"A Finite-Difference Trust-Region Method for Convexly Constrained Smooth Optimization","abstract":"We propose a derivative-free trust-region method based on finite-difference gradient approximations for smooth optimization problems with convex constraints. The proposed method does not require computing an approximate stationarity measure. For nonconvex problems, we establish a worst-case complexity bound of $\\mathcal{O}\\!\\left(n\\left(\\tfrac{L}σε\\right)^{-2}\\right)$ function evaluations for the method to reach an $\\left(\\tfrac{L}σε\\right)$-approximate stationary point, where $n$ is the number of variables, $L$ is the Lipschitz constant of the gradient, and $σ$ is a user-defined estimate of $L$. If the objective function is convex, the complexity to reduce the functional residual below $(L/σ)ε$ is shown to be of $\\mathcal{O}\\!\\left(n\\left(\\tfrac{L}σε\\right)^{-1}\\right)$ function evaluations, while for Polyak-Lojasiewicz functions on unconstrained domains, the bound further improves to $\\mathcal{O}\\left(n\\log\\left(\\left(\\frac{L}σε\\right)^{-1}\\right)\\right)$. Numerical experiments on benchmark problems and a model-fitting application demonstrate the method's efficiency relative to state-of-the-art derivative-free solvers for both unconstrained and bound-constrained problems.","short_abstract":"We propose a derivative-free trust-region method based on finite-difference gradient approximations for smooth optimization problems with convex constraints. The proposed method does not require computing an approximate stationarity measure. For nonconvex problems, we establish a worst-case complexity bound of $\\mathca...","url_abs":"https://arxiv.org/abs/2510.17366","url_pdf":"https://arxiv.org/pdf/2510.17366v1","authors":"[\"Dânâ Davar\",\"Geovani Nunes Grapiglia\"]","published":"2025-10-20T10:05:21Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}