Tolerances, robustness and parametrization of matrix properties related to optimization problems

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10401024" target="_blank" >RIV/00216208:11320/19:10401024 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=wL1gO75O3i" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=wL1gO75O3i</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1080/02331934.2018.1545837" target="_blank" >10.1080/02331934.2018.1545837</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Tolerances, robustness and parametrization of matrix properties related to optimization problems

Popis výsledku v původním jazyce

When we speak about parametric programming, sensitivity analysis or related topics, we usually mean the problem of studying specified perturbations of the data such that for a given optimization problem some optimality criterion remains satisfied. In this paper, we turn to another question. Suppose that A is a matrix having a specific property . What are the maximal allowable variations of the data such that the property still remains valid for the matrix? We study two basic forms of perturbations. The first is a perturbation in a given direction, which is closely related to parametric programming. The second type consists of all possible data variations in a neighbourhood specified by a certain matrix norm; this is related to the tolerance approach to sensitivity analysis or to stability. The matrix properties discussed in this paper are positive definiteness; M-matrix, H-matrix and P-matrix property; total positivity; inverse M-matrix property and inverse nonnegativity.

Název v anglickém jazyce

Tolerances, robustness and parametrization of matrix properties related to optimization problems

Popis výsledku anglicky

When we speak about parametric programming, sensitivity analysis or related topics, we usually mean the problem of studying specified perturbations of the data such that for a given optimization problem some optimality criterion remains satisfied. In this paper, we turn to another question. Suppose that A is a matrix having a specific property . What are the maximal allowable variations of the data such that the property still remains valid for the matrix? We study two basic forms of perturbations. The first is a perturbation in a given direction, which is closely related to parametric programming. The second type consists of all possible data variations in a neighbourhood specified by a certain matrix norm; this is related to the tolerance approach to sensitivity analysis or to stability. The matrix properties discussed in this paper are positive definiteness; M-matrix, H-matrix and P-matrix property; total positivity; inverse M-matrix property and inverse nonnegativity.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

50201 - Economic Theory

Projekt

<a href="/cs/project/GA18-04735S" target="_blank" >GA18-04735S: Nové přístupy pro relaxační a aproximační techniky v deterministické globální optimalizaci</a><br>

Návaznosti

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

Rok uplatnění

2019

Kód důvěrnosti údajů

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

Název periodika

Optimization

ISSN

0233-1934

e-ISSN

—

Svazek periodika

68

Číslo periodika v rámci svazku

2-3

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

24

Strana od-do

667-690

Kód UT WoS článku

000462381900013

EID výsledku v databázi Scopus

2-s2.0-85057306882