Effective Algorithms for Solving Trace Minimization Problem in Multivariate Statistics

Table 5

Comparison results of the considered algorithms.

	CT.	IT.	Grad.	Obj.
Algorithm 2	0.04	127/2	6.49 ×	−73.76
Algorithm 3	0.35	127/3	6.41 ×	−73.76
Existing-RTR	0.44	16	1.28 ×	−73.76
Existing-RBFGS	0.87	281	8.93 ×	−73.76
OptStiefel	0.04	270	1.27 ×	−73.76
RCG-Cayley	0.11	446	1.83 ×	−73.76
RCG-Pol	0.84	2000	7.87 ×	−73.75
RCG-QR	0.07	369	1.20 ×	−73.76
RGPRP-CG	0.04	233	1.45 ×	−73.76
RFR-CG	0.29	2000	1.32 ×	−73.76
Algorithm 2	0.19	140/4	9.86 ×	−76.97
Algorithm 3	0.63	140/5	5.89 ×	−76.97
Existing-RTR	0.57	15	2.95e − 10	−76.97
Existing-RBFGS	1.31	387	8.63 ×	−76.97
OptStiefel	0.19	501	1.26 ×	−76.97
RCG-Cayley	0.60	985	2.05 ×	−76.97
RCG-Pol	2.99	2000	1.64 ×	−76.95
RCG-QR	0.43	696	6.43 ×	−76.97
RGPRP-CG	0.15	353	1.32 ×	−76.97
RFR-CG	0.93	2000	3.93 ×	−76.87
Algorithm 2	1.74	258/4	5.72 ×	−79.90
Algorithm 3	1.15	258/5	7.54 ×	−79.90
Existing-RTR	0.82	18	3.29 ×	−79.90
Existing-RBFGS	2.96	676	8.33 ×	−79.90
OptStiefel	0.57	648	1.11 ×	−79.90
RCG-Cayley	1.45	1038	7.97 ×	−79.90
RCG-Pol	5.70	1604	7.51 ×	−79.87
RCG-QR	1.33	965	3.60 ×	−79.90
RGPRP-CG	0.49	511	1.46 ×	−79.90
RFR-CG	1.99	2000	5.32 ×	−79.90
Algorithm 2	4.60	157/4	5.25 ×	−81.55
Algorithm 3	1.55	157/5	9.16 ×	−81.55
Existing-RTR	1.06	15	4.85 ×	−81.55
Existing-RBFGS	3.58	650	8.95 ×	−81.55
OptStiefel	1.77	992	1.36 ×	−81.55
RCG-Cayley	2.09	749	2.03 ×	−81.55
RCG-Pol	15.14	2000	1.55 ×	−81.54
RCG-QR	1.95	703	1.34 ×	−81.55
RGPRP-CG	0.83	426	1.51 ×	−81.55
RFR-CG	3.87	2000	1.74 ×	−81.48
Algorithm 2	21.52	135/13	5.83 ×	−82.68
Algorithm 3	2.59	135/5	4.53 ×	−82.69
Existing-RTR	1.41	17	3.07 ×	−82.69
Existing-RBFGS	8.27	703	9.69 ×	−82.69
OptStiefel	3.41	529	2.76 ×	−82.69
RCG-Cayley	8.21	787	1.61 ×	−82.69
RCG-Pol	58.01	2000	6.95 ×	−82.67
RCG-QR	14.58	1420	1.15 ×	−82.69
RGPRP-CG	4.19	626	1.64 ×	−82.69
RFR-CG	15.72	2000	1.63 ×	−82.65
Algorithm 2	28.07	138/12	5.12 ×	−83.55
Algorithm 3	5.40	138/8	2.87 ×	−83.55
Existing-RTR	4.09	19	3.37 ×	−83.55
Existing-RBFGS	15.39	917	1.00 ×	−83.55
OptStiefel	13.00	1317	1.66 ×	−83.55
RCG-Cayley	29.72	1829	2.70 ×	−83.55
RCG-Pol	82.85	1838	3.66 ×	−83.54
RCG-QR	24.98	1569	4.00 ×	−83.55
RGPRP-CG	11.26	1051	1.22 ×	−83.55
RFR-CG	21.09	2000	1.88 ×	−83.48
Algorithm 2	56.49	147/14	8.44 ×	−84.25
Algorithm 3	6.28	147/9	4.36 ×	−84.25
Existing-RTR	2.97	20	9.91 ×	−84.25
Existing-RBFGS	16.56	800	9.75 ×	−84.25
OptStiefel	20.03	1436	1.28 ×	−84.25
RCG-Cayley	32.21	1427	2.60 ×	−84.25
RCG-Pol	125.53	2000	3.98 ×	−84.24
RCG-QR	24.08	1067	2.53 ×	−84.25
RGPRP-CG	17.47	1150	1.47 ×	−84.25
RFR-CG	30.46	2000	4.96 ×	−84.12
Algorithm 2	67.50	143/11	4.94 ×	−84.83
Algorithm 3	5.08	143/6	9.72 ×	−84.84
Existing-RTR	3.36	17	3.83 ×	−84.84
Existing-RBFGS	16.68	609	1.04 ×	−84.84
OptStiefel	13.63	720	1.22 ×	−84.84
RCG-Cayley	25.07	839	1.57 ×	−84.84
RCG-Pol	171.96	2000	1.53 ×	−84.82
RCG-QR	22.82	793	4.87 ×	−84.84
RGPRP-CG	14.48	717	1.35 ×	−84.84
RFR-CG	41.21	2000	9.98 ×	−84.81