On Coordinate-Wise Minimization Applied to General Convex Optimization Problems

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F20%3A00343072" target="_blank" >RIV/68407700:21230/20:00343072 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1016/j.procs.2020.09.142" target="_blank" >https://doi.org/10.1016/j.procs.2020.09.142</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.procs.2020.09.142" target="_blank" >10.1016/j.procs.2020.09.142</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On Coordinate-Wise Minimization Applied to General Convex Optimization Problems

Popis výsledku v původním jazyce

In this paper, we theoretically analyze principal properties of coordinate-wise minimization and we answer a few open questions related to it. In particular, we show that for minimizing any differentiable convex function on a given convex polyhedron, there exists a finite set of directions determined only by the polyhedron such that any local minimum with respect to these directions is a global minimum. We prove that the set of directions has a `nice’ structure for polyhedra defined by a k-regular matrix, which is a generalization of total unimodularity. We proceed to show that for some simple polyhedra, the number of these directions is polynomial, which subsumes already existing algorithms. We prove that the main result can not be extended for the case when the polyhedron is not known in advance or if the optimization is performed over a general convex set.

Název v anglickém jazyce

On Coordinate-Wise Minimization Applied to General Convex Optimization Problems

Popis výsledku anglicky

In this paper, we theoretically analyze principal properties of coordinate-wise minimization and we answer a few open questions related to it. In particular, we show that for minimizing any differentiable convex function on a given convex polyhedron, there exists a finite set of directions determined only by the polyhedron such that any local minimum with respect to these directions is a global minimum. We prove that the set of directions has a `nice’ structure for polyhedra defined by a k-regular matrix, which is a generalization of total unimodularity. We proceed to show that for some simple polyhedra, the number of these directions is polynomial, which subsumes already existing algorithms. We prove that the main result can not be extended for the case when the polyhedron is not known in advance or if the optimization is performed over a general convex set.

Druh

D - Stať ve sborníku

CEP obor

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OECD FORD obor

10100 - Mathematics

Projekt

<a href="/cs/project/GA19-09967S" target="_blank" >GA19-09967S: Hierarchické architektury pro rozpoznávání</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2020

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

Knowledge-Based and Intelligent Information & Engineering Systems: Proceedings of the 24th International Conference KES2020

ISBN

—

ISSN

1877-0509

e-ISSN

—

Počet stran výsledku

10

Strana od-do

1328-1337

Název nakladatele

Elsevier B.V.

Místo vydání

Amsterdam

Místo konání akce

Verona

Datum konání akce

16. 9. 2020

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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