On the Optimal Correction of Infeasible Systems of Linear Inequalities
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10437025" target="_blank" >RIV/00216208:11320/21:10437025 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Sv~HMmp-sv" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Sv~HMmp-sv</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10957-021-01868-1" target="_blank" >10.1007/s10957-021-01868-1</a>
Alternative languages
Result language
angličtina
Original language name
On the Optimal Correction of Infeasible Systems of Linear Inequalities
Original language description
We study the optimum correction of infeasible systems of linear inequalities through making minimal changes in the coefficient matrix and the right-hand side vector by using the Frobenius norm. It leads to a special structured unconstrained nonlinear and nonconvex problem, which can be reformulated as a one-dimensional parametric minimization problem such that each objective function corresponds to a trust region subproblem. We show that, under some assumptions, the parametric function is differentiable and strictly unimodal. We present optimally conditions, propose lower and upper bounds on the optimal value and discuss attainability of the optimal value. To solve the original problem, we propose a binary search method accompanied by a type of Newton-Lagrange method for solving the subproblem. The numerical results illustrate the effectiveness of the suggested method. (C) 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
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
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Optimization Theory and Applications
ISSN
0022-3239
e-ISSN
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Volume of the periodical
190
Issue of the periodical within the volume
1
Country of publishing house
US - UNITED STATES
Number of pages
24
Pages from-to
32-55
UT code for WoS article
000655087500001
EID of the result in the Scopus database
2-s2.0-85106502516