Table 2:

CPU times and optima for simplex-constrained least squares. Here $\mathit{A}\in {ℝ}^{n\times p}$, PD is the proximal distance algorithm, IPOPT is the Ipopt solver, and Gurobi is the Gurobi solver. After n = 1024, the predictor matrix A is sparse.

Dimensions		Optima			CPU Times
n	p	PD	IPOPT	Gurobi	PD	IPOPT	Gurobi
16	8	4.1515	4.1515	4.1515	0.0038	0.0044	0.0010
32	16	10.8225	10.8225	10.8225	0.0036	0.0039	0.0010
64	32	29.6218	29.6218	29.6218	0.0079	0.0079	0.0019
128	64	43.2626	43.2626	43.2626	0.0101	0.0078	0.0033
256	128	111.7642	111.7642	111.7642	0.0872	0.0151	0.0136
512	256	231.6455	231.6454	231.6454	0.1119	0.0710	0.0619
1024	512	502.1276	502.1276	502.1276	0.2278	0.4013	0.2415
2048	1024	994.2447	994.2447	994.2447	1.2575	2.3346	1.1682
4096	2048	2056.8381	2056.8381	2056.8381	1.3253	15.2214	7.4971
8192	4096	4103.4611	4103.4611	4103.4611	3.0289	146.1604	49.7411
16384	8192	8295.2136	8295.2136	8295.2136	6.8739	732.1039	412.3612