Computing Weighted Analytic Center for Linear Matrix Inequalities Using Infeasible Newton’s Method

Table 2

Infeasible Newton’s versus Standard Newton’s methods using different weights .

Problem	Weights	Inf. Newton; 1st feas. point; iter.	Inf. Newton; 1st feas. point; time (sec)	Inf. Newton; iter.	Inf. Newton; time (sec)	St. Newton; iter.	St. Newton; time (sec)
1	, 10	2	0.0185	4	0.0096	2	0.0056
2	, 100, 100, 1	3	17.2562			3	0.0161
3	, 1000	51	0.3771	46	0.1690	41	0.1042
4	, 10, 1	20	10.8898			9	0.0687
5	, 1, 10	2	8.8548			4	0.0215
6	1, , 1, 10, 100
7	100, 10,	129	9.5582			33	0.1810
8	1, 1000, , 10
9	, 1000, 1000	1	8.5943			4	0.0278
10	, 1000, 100, 1000, 100	6	25.3801			2	0.0158
11	, 10, 100, 1000, 1000, 10, 100
12	, 1, 100, 10, 1, 10	3	17.5497			5	0.0701
13	1000, , 1000, 100, 100
14	1, 1000, , 1000, 1
15	1, 1, 1, 100, , 100, 100, 10
16	10, 1, 10, 1000, 1000, 10, 1	24	0.2885	3	0.0234	5	0.2108
17	100, 100, 10, 1, 1000	3	0.0508	4	0.0252	3	0.0534
18	1, 1000	2	0.0286	6	0.0182	4	0.0579
19	100, 10, 1000, 1, 1000, 100, 100, 1000, 10	10	0.2117	7	0.0749	8	0.9943
20	1000, 1000	1	0.0180	4	0.0125	7	0.0664
21	1, 1, 10, 1, 100, 10, 1	21	0.3301	3	0.0342	3	0.4761
22	1, 1000, 100, 10, 1000, 1, 100, 100, 100, 1	7	0.2006	3	0.0491	3	0.2011
23	100, 10, 1, 1	4	0.0609	5	0.0231	6	0.0297
24	1000, 1	12	0.0564	2	0.0052	3	0.0348
25	1, 1, 10, 1, 1000, 1, 1, 10	8	0.1360	3	0.0280	3	0.0224
26	100, 1, 100, 1, 1, 1, 1, 1	20	0.2815	2	0.0208	3	0.3256
27	1, 1, 1, 10, 1, 10, 1, 100, 1, 10	8	0.3212	4	0.0945	6	2.1028
28	10, 10, 100, 1, 1, 1	7	0.0986	3	0.0246	4	0.0718
29	1, 1, 10	1	0.0092
30	10, 1	2	0.0268	4	0.0149	3	0.0121
31	1, 10, 1, 1	1	0.0444	4	0.0326	4	0.0270
32	100, 1, 10, 1	8	0.0994	4	0.0278	4	0.0444
33	100, 100, 1, 10	6	0.0612	3	0.0168	3	0.0318
34	1, 100, 1, 1, 1, 10, 100, 100, 10	7	0.1870	3	0.0426	5	0.9478
35	1, 10, 100, 1, 1	31	0.3678	2	0.0175	2	0.3845