Conditions When the Problems of Linear Programming Are Algorithmically Unsolvable-Reference-Cited by-同舟云学术

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Conditions When the Problems of Linear Programming Are Algorithmically Unsolvable

Published:2024-04-27 Issue:5 Volume:13 Page:293
ISSN:2075-1680
Container-title:Axioms
language:en
Short-container-title:Axioms

Author:

Chernov Viktor¹,Chernov Vladimir²^ORCID

Affiliation:

1. Department of Applied Mathematics and Economico-Mathematical Methods, St. Petersburg State University of Economics, Griboedov Canal emb., 30–32, St. Petersburg 191023, Russia

2. Mathematics Department, Dartmouth College, 6188 Kemeny Hall, Hanover, NH 03755, USA

Abstract

We study the properties of the constructive linear programming problems. The parameters of linear functions in such problems are constructive real numbers. Solving such a problem involves finding the optimal plan with the constructive real number components. We show that it is impossible to have an algorithm that solves an arbitrary constructive real programming problem.

Funder

Simons Foundation

Publisher

MDPI AG

Link

https://www.mdpi.com/2075-1680/13/5/293/pdf

Reference18 articles.

1. On constructive mathematics;Markov;Trudy Mat. Inst. Steklov,1962

2. On constructive functions;Markov;Trudy Mat. Inst. Steklov,1958

3. Constructive real numbers and constructive functional spaces;Sanin;Trudy Mat. Inst. Steklov,1962

4. Algorithmic operators in constructive complete separable metric spaces;Ceitin;Dokl. Akad. Nauk SSSR,1959

5. Mean-value theorems in constructive analysis;Ceitin;Trudy Mat. Inst. Steklov.,1962

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