An Accelerated Fixed-Point Algorithm Applied to Quadratic Convex Separable Knapsack Problems

Table 1

Uncorrelated tests for state-of-the-art algorithms.

Dimension	Iterations			Time (sec)			Error
	Avg	Max	Min	Avg	Max	Min	—
FPA2
500000	5.3	8	4	0.010	0.018	0.009	0
1000000	5.5	10	4	0.021	0.032	0.018	0
10000000	5.4	10	4	0.354	0.406	0.324	0
50000000	5.3	8	3	1.774	1.964	1.556	0
Newton
500000	5.3	8	4	0.018	0.023	0.015	0
1000000	5.5	10	4	0.038	0.047	0.030	0
10000000	5.2	10	4	0.434	0.535	0.346	0
50000000	5.2	7	3	2.181	2.649	1.555	0
Variable fixing
500000	8.8	11	8	0.022	0.025	0.021	0
1000000	9.0	12	7	0.047	0.053	0.041	0
10000000	9.3	12	8	0.539	0.622	0.468	0
50000000	9.5	11	8	2.718	3.065	2.377	0
FPA
500000	5.3	8	4	0.011	0.020	0.010	0
1000000	5.5	10	4	0.023	0.036	0.020	0
10000000	5.4	10	4	0.416	0.482	0.377	0
50000000	5.3	8	3	2.078	2.360	1.904	0
Secant
500000	8.7	14	7	0.020	0.028	0.014	0
1000000	8.6	13	6	0.041	0.059	0.029	0
10000000	8.5	14	7	0.443	0.658	0.285	0
50000000	8.5	12	6	2.323	3.254	1.426	0
Median search
500000	19.9	20	19	0.037	0.040	0.032	0
1000000	20.8	21	20	0.077	0.085	0.067	0
10000000	24.3	25	24	0.895	1.010	0.785	0
50000000	26.7	27	26	4.562	5.059	4.189	0