{"ID":2881278,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.13302","arxiv_id":"2508.13302","title":"First Order Algorithm on an Optimization Problem with Improved Convergence when Problem is Convex","abstract":"We propose a first order algorithm, a modified version of FISTA, to solve an optimization problem with an objective function that is a sum of a possibly nonconvex function, with Lipschitz continuous gradient, and a convex function which can be nonsmooth. The algorithm is shown to have an iteration complexity of $\\mathcal{O}(ε^{-2})$ to find an $ε$-approximate solution to the problem, and this complexity improves to $\\mathcal{O}(ε^{-2/3})$ when the objective function turns out to be convex. We further provide asymptotic convergence rate for the algorithm of worst case $o(ε^{-2})$ iterations to find an $ε$-approximate solution to the problem, with worst case $o(ε^{-2/3})$ iterations when its objective function is convex.","short_abstract":"We propose a first order algorithm, a modified version of FISTA, to solve an optimization problem with an objective function that is a sum of a possibly nonconvex function, with Lipschitz continuous gradient, and a convex function which can be nonsmooth. The algorithm is shown to have an iteration complexity of $\\mathc...","url_abs":"https://arxiv.org/abs/2508.13302","url_pdf":"https://arxiv.org/pdf/2508.13302v1","authors":"[\"Chee-Khian Sim\"]","published":"2025-08-18T18:42:50Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}