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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2501.18454 |
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| _version_ | 1866918249303638016 |
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| author | Woodstock, Zev |
| author_facet | Woodstock, Zev |
| contents | This note demonstrates that, for all compact convex sets, high-precision linear minimization can be performed via a single evaluation of the projection and a scalar-vector multiplication. In consequence, if $\varepsilon$-approximate linear minimization takes at least $L(\varepsilon)$ real vector-arithmetic operations and projection requires $P$ operations, then $\mathcal{O}(P)\geq \mathcal{O}(L(\varepsilon))$ is guaranteed. This concept is expounded with examples, an explicit error bound, and an exact linear minimization result for polyhedral sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_18454 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | High-precision linear minimization is no slower than projection Woodstock, Zev Optimization and Control 90C30, 03D15, 47N10, 52A07 This note demonstrates that, for all compact convex sets, high-precision linear minimization can be performed via a single evaluation of the projection and a scalar-vector multiplication. In consequence, if $\varepsilon$-approximate linear minimization takes at least $L(\varepsilon)$ real vector-arithmetic operations and projection requires $P$ operations, then $\mathcal{O}(P)\geq \mathcal{O}(L(\varepsilon))$ is guaranteed. This concept is expounded with examples, an explicit error bound, and an exact linear minimization result for polyhedral sets. |
| title | High-precision linear minimization is no slower than projection |
| topic | Optimization and Control 90C30, 03D15, 47N10, 52A07 |
| url | https://arxiv.org/abs/2501.18454 |