{"ID":2879805,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.15446","arxiv_id":"2508.15446","title":"A smoothed proximal trust-region algorithm for nonconvex optimization problems with $L^p$-regularization, $p\\in (0,1)$","abstract":"We investigate a trust-region algorithm to solve a nonconvex optimization problem with $L^p$-regularization for $p\\in(0,1)$. The algorithm relies on descent properties of a so-called generalized Cauchy point that can be obtained efficiently by a line search along a suitable proximal path. To handle the nonconvexity and nonsmoothness of the $L^p$-pseudonorm, we replace it by a smooth approximation and construct a convex upper bound of that approximation. This enables us to use results of a trust-region method for composite problems with a convex nonsmooth term. We prove convergence properties of the resulting smoothed proximal trust-region algorithm and investigate its performance in some numerical examples. Furthermore, approximate subproblem solvers for the arising trust-region subproblems are considered.","short_abstract":"We investigate a trust-region algorithm to solve a nonconvex optimization problem with $L^p$-regularization for $p\\in(0,1)$. The algorithm relies on descent properties of a so-called generalized Cauchy point that can be obtained efficiently by a line search along a suitable proximal path. To handle the nonconvexity and...","url_abs":"https://arxiv.org/abs/2508.15446","url_pdf":"https://arxiv.org/pdf/2508.15446v1","authors":"[\"Harbir Antil\",\"Anna Lentz\"]","published":"2025-08-21T11:08:32Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}