Publication at Faculty of Mathematics and Physics |
2017
Abstract
Interval linear programming provides a mathematical tool for handling linear optimization problems affected by uncertainty. Contrarily to classical linear programming, the properties of interval linear programs depend on the form in which the program is given.
In this paper, we study how the transformations used in linear programming - imposing non-negativity, changing equations to inequalities and vice versa - affect the optimal set of an interval program. Since the results are mostly negative in the general case, we also consider interval linear programs with a fixed coefficient matrix.
For this special case, we prove that all transformations preserve the optimal solution set.