Optimal iterative QP and QPQC algorithms

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27240%2F13%3A86092242" target="_blank" >RIV/61989100:27240/13:86092242 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/61989100:27740/13:86092242

Výsledek na webu

<a href="http://link.springer.com/article/10.1007%2Fs10479-013-1479-0#" target="_blank" >http://link.springer.com/article/10.1007%2Fs10479-013-1479-0#</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10479-013-1479-0" target="_blank" >10.1007/s10479-013-1479-0</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Optimal iterative QP and QPQC algorithms

Popis výsledku v původním jazyce

We review our recent results in the development of optimal algorithms for the minimization of a strictly convex quadratic function subject to separable convex inequality constraints and/or linear equality constraints. A unique feature of our algorithms is the theoretically supported bound on the rate of convergence in terms of the bounds on the spectrum of the Hessian of the cost function, independent of representation of the constraints. When applied to the class of convex QP or QPQC problems with the spectrum in a given positive interval and a sparse Hessian matrix, the algorithms enjoy optimal complexity, i.e., they can find an approximate solution at the cost that is proportional to the number of unknowns. The algorithms do not assume representation of the linear equality constraints by full rank matrices. The efficiency of our algorithms is demonstrated by the evaluation of the projection of a point to the intersection of the unit cube and unit sphere with hyperplanes.

Název v anglickém jazyce

Optimal iterative QP and QPQC algorithms

Popis výsledku anglicky

We review our recent results in the development of optimal algorithms for the minimization of a strictly convex quadratic function subject to separable convex inequality constraints and/or linear equality constraints. A unique feature of our algorithms is the theoretically supported bound on the rate of convergence in terms of the bounds on the spectrum of the Hessian of the cost function, independent of representation of the constraints. When applied to the class of convex QP or QPQC problems with the spectrum in a given positive interval and a sparse Hessian matrix, the algorithms enjoy optimal complexity, i.e., they can find an approximate solution at the cost that is proportional to the number of unknowns. The algorithms do not assume representation of the linear equality constraints by full rank matrices. The efficiency of our algorithms is demonstrated by the evaluation of the projection of a point to the intersection of the unit cube and unit sphere with hyperplanes.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/ED1.1.00%2F02.0070" target="_blank" >ED1.1.00/02.0070: Centrum excelence IT4Innovations</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2013

Kód důvěrnosti údajů

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

Název periodika

Annals of Operations Research

ISSN

0254-5330

e-ISSN

—

Svazek periodika

Neuveden

Číslo periodika v rámci svazku

October 2013

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

14

Strana od-do

1-14

Kód UT WoS článku

000382679800002

EID výsledku v databázi Scopus

2-s2.0-84979530049