{"paper":{"title":"The Method of Ellipcenters for strongly convex minimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The Method of Ellipcenters converges linearly for any differentiable strongly convex objective.","cross_cats":[],"primary_cat":"math.OC","authors_text":"Eduarda Ferreira, Ramyro Correa, Roger Behling, Vincent Guigues","submitted_at":"2026-05-12T23:30:07Z","abstract_excerpt":"This work is about ME, the Method of Ellipcenters. ME was recently introduced by these very authors as a first order accelerated scheme for unconstrained minimization. Its iterates are all centers of ellipses carefully designed to somehow capture ill-conditioning of the underlying optimization problem. In the first article on ME, we were able to prove that it converges with linear rate when the objective function is quadratic and strongly convex, while here we derive convergence for any differentiable strongly convex objective. This investigation was inspired by the great performance of ME in "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"we derive convergence for any differentiable strongly convex objective","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That ellipses can be constructed at each step to capture the ill-conditioning of an arbitrary differentiable strongly convex function while preserving the linear rate.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"ME achieves linear convergence for any differentiable strongly convex objective by centering iterates inside carefully chosen ellipses.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The Method of Ellipcenters converges linearly for any differentiable strongly convex objective.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"8ae79aed078c66456e9dbcbdd8216c1c97f064b37b068c88d15e545f89af3d76"},"source":{"id":"2605.12820","kind":"arxiv","version":1},"verdict":{"id":"a8693639-17a0-4946-a468-750632053cad","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T19:32:12.041251Z","strongest_claim":"we derive convergence for any differentiable strongly convex objective","one_line_summary":"ME achieves linear convergence for any differentiable strongly convex objective by centering iterates inside carefully chosen ellipses.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That ellipses can be constructed at each step to capture the ill-conditioning of an arbitrary differentiable strongly convex function while preserving the linear rate.","pith_extraction_headline":"The Method of Ellipcenters converges linearly for any differentiable strongly convex objective."},"references":{"count":18,"sample":[{"doi":"","year":2025,"title":"Introducing the method of ellipcenters, a new first order technique for unconstrained optimization.arXiv, 2025","work_id":"c4cbd59c-3022-4100-a06d-1f19779b82cc","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1988,"title":"Two-Point Step Size Gradient Methods.IMA Journal of Numerical Analysis, 8(1):141–148, 1988","work_id":"be5eaf88-5c64-4c93-8ea4-129ea47b55f1","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2009,"title":"IMAGING SCIENCES, 2 (1):183-202, 2009","work_id":"531d720c-2005-43a5-bd3a-4b7a42d17640","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"M´ ethode g´ en´ erale pour la r´ esolution des syst` emes d’´ equations simultan´ ees","work_id":"9a725802-dd94-40ee-abc7-a06928e5964b","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1987,"title":"Practical Methods of Optimization (2nd ed.)New York: John Wiley & Son, 1987","work_id":"a9338e2f-d654-4205-a98b-6a129d9705ed","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":18,"snapshot_sha256":"5500ba8f7e0d591f545eefc92eae7e9b1aa684d43fb8ab1a1c87b418c2911456","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"27fd2771551744247b65e9ac4d5ab9c05bc6eb699ce6b711e55dd8741e7a8927"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}