Solving interval linear programming problems with equality constraints using extended interval enclosure solutions

Abstract

This paper focuses on solving systems of interval linear equations and interval linear programming in a computationally efficient way. Since the computational complexity of most interval enclosure numerical methods is often prohibitive, a procedure to obtain a relaxation of the interval enclosure solution that is computationally tractable is proposed. We show that our approach unifies the four standard interval solutions—the weak, strong, control and tolerance solutions. The interval linear system methods require $n\cdot 2^{n}$ linear solutions. However, in the case of linear programming problems, we show that this requires just two optimization problem of the size of the problem itself. Numerical examples illustrate our results.

Appendix

See Tables 1, 2, 3, 4 and Fig. 1.

Table 1 A comparison of IE and the extended IE is as follows

Table 2 Some numerical examples to compare the IE and EIE solutions

Table 3 A numerical example

Table 4 A new examples

Fig. 1

The solution using INTLAB with both the IE and extended IE solutions