A New Technique for Determining Approximate Center of a Polytope

Table 4

Comparison of average number of iterations for higher dimensional random LPs.

Order	P-center	CN-center
3 × 5	62.71	16.57
5 × 3	35.85	8.23
5 × 5	85.5	55.33
10 × 5	136.8	34.4
10 × 10	476.44	77.22
15 × 15	650.71	249.85
15 × 10	348.6	96.34
20 × 20	331.44	258.88
30 × 20	213.2	162.7
20 × 30	508.2	236
30 × 30	206.75	193.125

Note: here, is more than enough. If we observe the convergence pattern of CN-center, we can see that convergence is initially fast and gets slower in later iterations. Generally, we do not need exact central point; for practical purposes, any good central location is enough for working. So a good central point is obtainable by CN-center within just a few iterations for a 100 × 100 or even a very high dimensional problem.