Testing weak optimality of a given solution in interval linear programming revisited: NP-hardness proof, algorithm and some polynomial cases

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Main Authors: Rada, Miroslav, Hladík, Milan, Garajová, Elif
Format: Preprint
Published: 2017
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author Rada, Miroslav
Hladík, Milan
Garajová, Elif
author_facet Rada, Miroslav
Hladík, Milan
Garajová, Elif
contents We address the problem of testing weak optimality of a given solution of a given interval linear program. The problem was recently wrongly stated to be polynomially solvable. We disprove it. We show that the problem is NP-hard in general. We propose a new algorithm for the problem, based on orthant decomposition and solving linear systems. Running time of the algorithm is exponential in the number of equality constraints. Interval linear programs with inequality constraints only can be processed in polynomial time.
format Preprint
id arxiv_https___arxiv_org_abs_1712_00350
institution arXiv
publishDate 2017
record_format arxiv
spellingShingle Testing weak optimality of a given solution in interval linear programming revisited: NP-hardness proof, algorithm and some polynomial cases
Rada, Miroslav
Hladík, Milan
Garajová, Elif
Optimization and Control
65G40, 90C31
We address the problem of testing weak optimality of a given solution of a given interval linear program. The problem was recently wrongly stated to be polynomially solvable. We disprove it. We show that the problem is NP-hard in general. We propose a new algorithm for the problem, based on orthant decomposition and solving linear systems. Running time of the algorithm is exponential in the number of equality constraints. Interval linear programs with inequality constraints only can be processed in polynomial time.
title Testing weak optimality of a given solution in interval linear programming revisited: NP-hardness proof, algorithm and some polynomial cases
topic Optimization and Control
65G40, 90C31
url https://arxiv.org/abs/1712.00350