Pointwise residual method for solving primal and dual ill-posed linear programming problems with approximate data

A. Y. Ivanitskiy; V. V. Ejov; F. P.  Vasilyev

doi:10.21914/anziamj.v62.14839

Authors

A. Y. Ivanitskiy Chuvash State University https://orcid.org/0000-0003-3148-1858
V. V. Ejov Flinders University http://orcid.org/0000-0002-5582-2859
F. P. Vasilyev Moscow State University https://orcid.org/0000-0002-4126-0242

DOI:

https://doi.org/10.21914/anziamj.v62.14839

Keywords:

ill-posed linear programming problems, approximate data, pointwise residual method, primal and dual linear programming problems

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.

doi:10.1017/S1446181120000243

Author Biographies

A. Y. Ivanitskiy, Chuvash State University

Faculty of Applied Mathematics, Physics and Information Technology, Chuvash State University, Cheboksary, Russia.

V. V. Ejov, Flinders University

Mathematical Sciences Laboratory, Flinders University, College of Science and Engineering, Tonsley, South Australia, Australia.

F. P. Vasilyev, Moscow State University

Department of Mathematical Analysis, Faculty of Computational Mathematics and Cybernetics, Moscow State University, Leninskie Gory, 1, Moscow, Russia.