2025/10/20 by Dânâ Davar, Davar, Dânâ, Geovani Nunes Grapiglia +1
Computer Science · Engineering · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques #Stochastic Gradient Optimization Techniques
paper · pdf · doi:10.48550/arxiv.2510.17366
openalex publication_date 2025/10/20 · openalex created_date 2025/10/22 · openalex updated_date 2026/07/28
We propose a derivative-free trust-region method based on finite-difference gradient approximations for smooth optimization problems with convex constraints. For nonconvex problems, we establish a worst-case complexity bound of O (n(\fracLσε)-2) function evaluations for the method to reach an (\fracLσε)-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 O (n(\fracLσε)-1) function evaluations, while for Polyak-Lojasiewicz functions on unconstrained domains, the bound further improves to O(nlog((\fracLσε)-1)). Numerical experiments on benchmark problems with noise-free and noisy objective functions, as well as a model-fitting application, show the efficiency of the proposed method relative to state-of-the-art derivative-free solvers for unconstrained and bound-constrained problems.