University of Kashan Mathematics Interdisciplinary Research 2538-3639 11 3 2026 09 01 An Efficient Algorithm Based on Descent Direction for Nonsmooth Optimization and its Application in Image Restoration 253 271 115673 10.22052/mir.2026.257676.1545 EN Kimia Hoseinpour ‎Department of Applied Mathematics, ‎Faculty of Mathematical Sciences,‎ ‎University of Mazandaran, ‎Babolsar‎, ‎I‎. ‎R‎. ‎Iran Zohreh Akbari ‎Department of Applied Mathematics, ‎Faculty of Mathematical Sciences,‎ ‎University of Mazandaran, ‎Babolsar‎, ‎I‎. ‎R‎. ‎Iran Journal Article 2025 09 29 ‎In this paper‎, ‎we propose a novel descent-based hybrid algorithm for solving nonsmooth box-constrained optimization problems‎. ‎The method combines an $\varepsilon$-subdifferential approximation with heuristic local and global line search strategies‎. ‎Theoretical analysis establishes the global convergence‎ ‎of the algorithm‎ ‎under Fritz John optimality conditions‎. ‎To demonstrate the effectiveness of the proposed approach‎, ‎it is applied to several standard grayscale test images for denoising purposes‎, ‎addressing various types of noise‎, ‎including Gaussian and salt-and-pepper noise‎. ‎Moreover‎, ‎extensive experiments and comparative analyses with existing denoising algorithms confirm the superior performance of our method in terms of restoration quality‎, ‎particularly with respect to PSNR and SSIM metrics‎. https://mir.kashanu.ac.ir/article_115673_43fcca62cef0ea220f5cf6845c5a50d1.pdf