Tolerances, robustness and parametrization of matrix properties related to optimization problems
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Tolerances, robustness and parametrization of matrix properties related to optimization problems
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
50201 - Economic Theory
Result continuities
Project
<a href="/en/project/GA18-04735S" target="_blank" >GA18-04735S: Novel approaches for relaxation and approximation techniques in deterministic global optimization</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Optimization
ISSN
0233-1934
e-ISSN
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Volume of the periodical
68
Issue of the periodical within the volume
2-3
Country of publishing house
GB - UNITED KINGDOM
Number of pages
24
Pages from-to
667-690
UT code for WoS article
000462381900013
EID of the result in the Scopus database
2-s2.0-85057306882