High-precision linear minimization is no slower than projection

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Detalles Bibliográficos
Autor principal:	Woodstock, Zev
Formato:	Preprint
Publicado:	2025
Materias:	Optimization and Control 90C30, 03D15, 47N10, 52A07
Acceso en línea:	Acceder al recurso
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

_version_	1866918249303638016
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

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