{"paper":{"title":"Nesterov Finds GRAAL: Optimal and Adaptive Gradient Method for Convex Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"math.OC","authors_text":"Dmitry Kovalev, Ekaterina Borodich","submitted_at":"2025-07-13T23:07:45Z","abstract_excerpt":"In this paper, we focus on the problem of minimizing a continuously differentiable convex objective function, $\\min_x f(x)$. Recently, Malitsky (2020); Alacaoglu et al.(2023) developed an adaptive first-order method, GRAAL. This algorithm computes stepsizes by estimating the local curvature of the objective function without any line search procedures or hyperparameter tuning, and attains the standard iteration complexity $\\mathcal{O}(L\\lVert x_0-x^*\\rVert^2/\\epsilon)$ of fixed-stepsize gradient descent for $L$-smooth functions. However, a natural question arises: is it possible to accelerate t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.09823","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.09823/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}