Table 1:

CPU times and optima for linear programming. Here m is the number of constraints, n is the number of variables, PD1 is the proximal distance algorithm over an affine domain, PD2 is the proximal distance algorithm over a nonnegative domain, SCS is the Splitting Cone Solver, and Gurobi is the Gurobi solver. After m = 512 the constraint matrix A is initialized to be sparse with sparsity level s = 0.01.

Dimensions		Optima				CPU Times (secs)
m	n	PD1	PD2	SCS	Gurobi	PD1	PD2	SCS	Gurobi
2	4	0.2629	0.2629	0.2629	0.2629	0.0142	0.0010	0.0034	0.0038
4	8	1.0455	1.0457	1.0456	1.0455	0.0212	0.0021	0.0009	0.0011
8	16	2.4513	2.4515	2.4514	2.4513	0.0361	0.0048	0.0018	0.0029
16	32	3.4226	3.4231	3.4225	3.4223	0.0847	0.0104	0.0090	0.0036
32	64	6.2398	6.2407	6.2397	6.2398	0.1428	0.0151	0.0140	0.0055
64	128	14.671	14.674	14.671	14.671	0.2117	0.0282	0.0587	0.0088
128	256	27.116	27.125	27.116	27.116	0.3993	0.0728	0.8436	0.0335
256	512	58.501	58.512	58.494	58.494	0.7426	0.1538	2.5409	0.1954
512	1024	135.35	135.37	135.34	135.34	1.6413	0.5799	5.0648	1.7179
1024	2048	254.50	254.55	254.47	254.48	2.9541	3.2127	3.9433	0.6787
2048	4096	533.29	533.35	533.23	533.23	7.3669	17.318	25.614	5.2475
4096	8192	991.78	991.88	991.67	991.67	30.799	95.974	98.347	46.957
8192	16384	2058.8	2059.1	2058.5	2058.5	316.44	623.42	454.23	400.59