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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*
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, SA5042, Australia; e-mail: vladimir.ejov@flinders.edu.au. Department of Mathematical Analysis, Faculty of Computational Mathematics and Cybernetics, Moscow State University, Leninskie Gory, 1, Moscow119234, 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, Moscow119234, Russia; e-mail: vasiliev.fp@gmail.ru.

Abstract

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.

MSC classification

Type
Research Article
Copyright
© Australian Mathematical Society 2021

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