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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.00741 |
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| _version_ | 1866910027539808256 |
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| author | Felzenszwalb, Pedro Lee, Heon |
| author_facet | Felzenszwalb, Pedro Lee, Heon |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_00741 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Projected Subgradient Ascent for Convex Maximization Felzenszwalb, Pedro Lee, Heon Optimization and Control Numerical Analysis 90C99 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. |
| title | Projected Subgradient Ascent for Convex Maximization |
| topic | Optimization and Control Numerical Analysis 90C99 |
| url | https://arxiv.org/abs/2511.00741 |