An Implementable First-Order Primal-Dual Algorithm for Structured Convex Optimization

Table 1

Numerical results for stable principal component pursuit problem.

𝑛	APGM				CPPA
	Iter.	rel𝐿	rel𝑆	CPU(s)	Iter.	rel𝐿	rel𝑆	CPU(s)
Rank𝑟=0.01,Card𝑟=0.01
50	84	9.36𝑒−003	2.67𝑒−005	0.2	88	9.15𝑒−003	2.29𝑒−005	0.2
100	44	8.41𝑒−003	2.47𝑒−005	0.6	52	8.38𝑒−003	1.87𝑒−005	0.6
150	58	5.00𝑒−003	2.16𝑒−005	2.1	57	4.89𝑒−003	1.87𝑒−005	2.0
200	52	4.81𝑒−003	2.01𝑒−005	4.1	45	4.42𝑒−003	2.36𝑒−005	3.4
250	52	3.40𝑒−003	1.97𝑒−005	7.4	46	3.14𝑒−003	2.42𝑒−005	6.4
300	47	3.30𝑒−003	1.90𝑒−005	11.4	42	2.53𝑒−003	3.58𝑒−005	9.8
400	43	2.57𝑒−003	1.83𝑒−005	39.1	42	1.66𝑒−003	4.18𝑒−005	37.7
500	38	2.08𝑒−003	2.77𝑒−005	82.1	42	1.13𝑒−003	4.68𝑒−005	89.2
Rank𝑟=0.02,Card𝑟=0.02
50	65	1.38𝑒−002	3.24𝑒−005	0.2	78	1.32𝑒−002	2.68𝑒−005	0.2
100	72	7.05𝑒−003	2.71𝑒−005	1.1	68	6.77𝑒−003	2.27𝑒−005	1.0
150	63	4.88𝑒−003	2.69𝑒−005	2.8	48	4.61𝑒−003	2.42𝑒−005	2.1
200	53	3.66𝑒−003	2.52𝑒−005	7.4	43	3.24𝑒−003	4.50𝑒−005	5.4
250	47	2.98𝑒−003	2.62𝑒−005	7.3	43	2.10𝑒−003	4.51𝑒−005	6.7
300	41	2.55𝑒−003	3.02𝑒−005	10.4	43	1.58𝑒−003	5.38𝑒−005	10.8
400	34	1.70𝑒−003	4.95𝑒−005	32.5	44	1.14𝑒−003	5.74𝑒−005	41.9
500	34	7.67𝑒−004	4.88𝑒−005	75.3	45	9.18𝑒−004	5.73𝑒−005	101.0
Rank𝑟=0.03,Card𝑟=0.03
50	98	9.03𝑒−003	3.91𝑒−005	0.4	88	8.86𝑒−003	3.09𝑒−005	0.3
100	78	6.41𝑒−003	3.18𝑒−005	1.3	64	6.13𝑒−003	2.62𝑒−005	1.0
150	56	3.67𝑒−003	3.42𝑒−005	2.5	51	3.41𝑒−003	2.97𝑒−005	2.2
200	45	3.09𝑒−003	3.32𝑒−005	4.2	46	2.54𝑒−003	3.94𝑒−005	4.0
250	38	2.16𝑒−003	4.35𝑒−005	6.1	46	1.67𝑒−003	4.94𝑒−005	7.1
300	35	1.71𝑒−003	4.86𝑒−005	8.7	46	1.32𝑒−003	5.39𝑒−005	11.5
400	34	1.22𝑒−003	8.13𝑒−005	31.9	47	9.56𝑒−004	5.85𝑒−005	45.4
500	34	9.29𝑒−004	8.18𝑒−005	74.5	47	8.43𝑒−004	6.44𝑒−005	106.4