On the Optimal Correction of Infeasible Systems of Linear Inequalities

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

On the Optimal Correction of Infeasible Systems of Linear Inequalities

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

On the Optimal Correction of Infeasible Systems of Linear Inequalities

Popis výsledku anglicky

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.

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

2021

Kód důvěrnosti údajů

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

Název periodika

Journal of Optimization Theory and Applications

ISSN

0022-3239

e-ISSN

—

Svazek periodika

190

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

24

Strana od-do

32-55

Kód UT WoS článku

000655087500001

EID výsledku v databázi Scopus

2-s2.0-85106502516