{"ID":2847366,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.00741","arxiv_id":"2511.00741","title":"Projected Subgradient Ascent for Convex Maximization","abstract":"We consider the problem of maximizing a convex function over a closed convex set in a real Hilbert space. For linear functions, we show that a single orthogonal projection suffices to obtain an approximate solution. For continuous convex functions over convex sets, we show that projected subgradient ascent converges to a first-order stationary point when using arbitrarily large step sizes. Taking the step sizes to infinity leads to a deterministic variant of the conditional gradient algorithm, and iterated linear optimization as a special case.","short_abstract":"We consider the problem of maximizing a convex function over a closed convex set in a real Hilbert space. For linear functions, we show that a single orthogonal projection suffices to obtain an approximate solution. For continuous convex functions over convex sets, we show that projected subgradient ascent converges to...","url_abs":"https://arxiv.org/abs/2511.00741","url_pdf":"https://arxiv.org/pdf/2511.00741v2","authors":"[\"Pedro Felzenszwalb\",\"Heon Lee\"]","published":"2025-11-01T23:52:20Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"math.NA\"]","methods":"[]","has_code":false}