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POINTWISE RESIDUAL METHOD FOR SOLVING PRIMAL AND DUAL ILL-POSED LINEAR PROGRAMMING PROBLEMS WITH APPROXIMATE DATA

Published online by Cambridge University Press:  12 January 2021

A. Y. IVANITSKIY Open the ORCID record for A. Y. IVANITSKIY [Opens in a new window] ,
V. V. EJOV Open the ORCID record for V. V. EJOV [Opens in a new window]  and
F. P. VASILYEV Open the ORCID record for F. P. VASILYEV [Opens in a new window]
A. Y. IVANITSKIY*
Affiliation:
Faculty of Applied Mathematics, Physics and Information Technology, Chuvash State University, Cheboksary, Russia.
V. V. EJOV
Affiliation:
Mathematical Sciences Laboratory at Flinders University of South Australia, College of Science and Engineering, 1284 South Road, Tonsley, SA 5042, Australia; e-mail: vladimir.ejov@flinders.edu.au. Department of Mathematical Analysis, Faculty of Computational Mathematics and Cybernetics, Moscow State University, Leninskie Gory, 1, Moscow 119234, Russia; e-mail: vasiliev.fp@gmail.ru.
F. P. VASILYEV
Affiliation:
Department of Mathematical Analysis, Faculty of Computational Mathematics and Cybernetics, Moscow State University, Leninskie Gory, 1, Moscow 119234, Russia; e-mail: vasiliev.fp@gmail.ru.
*
e-mail: ivanitskiy@hotmail.com
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Abstract

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We propose a variation of the pointwise residual method for solving primal and dual ill-posed linear programming with approximate data, sensitive to small perturbations. The method leads to an auxiliary problem, which is also a linear programming problem. Theorems of existence and convergence of approximate solutions are established and optimal estimates of approximation of initial problem solutions are achieved.

Keywords

ill-posed linear programming problemsapproximate datapointwise residual methodprimal and dual linear programming problems

MSC classification

Primary: 90C05: Linear programming

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 62 , Issue 3 , July 2020 , pp. 302 - 317
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Copyright
© Australian Mathematical Society 2021

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