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:10.1017/S1446181120000243

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

College of Science and Engineering

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	302-317
Number of pages	16
Journal	The ANZIAM Journal
Volume	62
Issue number	3
DOIs	https://doi.org/10.1017/S1446181120000243
Publication status	Published - Jul 2020

Keywords

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

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10.1017/S1446181120000243Licence: In Copyright

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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.",

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AU - Ejov, V. V.

AU - Vasilyev, F. P

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N2 - 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.

AB - 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.

KW - ill-posed linear programming problems

KW - approximate data

KW - pointwise residual method

KW - primal linear programming problems

KW - dual linear programming problems

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DO - 10.1017/S1446181120000243

M3 - Article

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EP - 317

JO - The ANZIAM Journal

JF - The ANZIAM Journal

IS - 3

ER -

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

Abstract

Keywords

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