{"ID":2878230,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.19234","arxiv_id":"2508.19234","title":"A New Inexact Manifold Proximal Linear Algorithm with Adaptive Stopping Criteria","abstract":"This paper proposes a new inexact manifold proximal linear (IManPL) algorithm for solving nonsmooth, nonconvex composite optimization problems over an embedded submanifold. At each iteration, IManPL solves a convex subproblem inexactly, guided by two adaptive stopping criteria. We establish convergence guarantees and show that IManPL achieves the best first-order oracle complexity for solving this class of problems. Numerical experiments on sparse spectral clustering and sparse principal component analysis demonstrate that our methods outperform existing approaches.","short_abstract":"This paper proposes a new inexact manifold proximal linear (IManPL) algorithm for solving nonsmooth, nonconvex composite optimization problems over an embedded submanifold. At each iteration, IManPL solves a convex subproblem inexactly, guided by two adaptive stopping criteria. We establish convergence guarantees and s...","url_abs":"https://arxiv.org/abs/2508.19234","url_pdf":"https://arxiv.org/pdf/2508.19234v2","authors":"[\"Zhong Zheng\",\"Xin Yu\",\"Shiqian Ma\",\"Lingzhou Xue\"]","published":"2025-08-26T17:54:57Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}