A New Spatial Branch and Bound Algorithm for Quadratic Program with One Quadratic Constraint and Linear Constraints

Table 1

Comparisons between SOCP_BB and SDP_BB.

n	SOCP_BB		SDP_BB
	Exp nodes	CPU time	Exp nodes	CPU time
10	109	4.4539	208	50.0983
10	1	0.0240	1	0.0698
10	128	5.1209	230	41.2431
10	92	3.4678	75	11.5937
10	1	0.0228	2	0.1881
20	125	8.3562	176	69.9982
20	1664	115.1088	3114	1067.7725
20	566	38.1457	991	330.2524
20	30	1.9629	54	13.2143
20	55	3.5615	134	31.8341
30	1	0.08702	2	0.5089
30	114	9.6467	272	179.0759
30	4389	419.0829	3910	1431.4212
30	70	5.9402	92	34.3371
30	2983	260.3418	7523	4909.2678
40	21	2.8233	52	29.3877
40	54	6.5244	214	121.6062
40	74	8.3827	185	110.2765
40	136	15.4152	252	156.2269
40	31	3.3112	200	119.5072
50	152	24.5512	483	456.7316
50	139	21.9021	445	411.3182
50	1	0.3228	1	0.4154
50	150	23.5961	210	187.4114
50	19	3.9621	107	104.7606
60	13	2.3786	59	82.2647
60	5	1.1534	35	54.2444
60	103	18.7057	305	426.8943
60	18	4.1163	63	93.2252
60	19	4.2133	79	113.4004
70	5434	1332.6043	—	—
70	32	7.8642	203	432.7264
70	3677	891.9838	—	—
70	60	14.3761	111	250.3169
70	258	57.3409	724	1556.7962
80	11	4.1058	27	78.7600
80	69	17.6592	306	948.1594
80	136	45.5027	607	1896.2123
80	12634	4315.1516	—	—
80	81	24.2367	626	1829.0213
90	1979	820.2060	758	3708.4941
90	13148	4698.9012	—	—
90	3563	1322.3103	—	—
90	13469	4953.5129	—	—
90	151	54.3170	1814	8381.2107
100	23	12.6613	161	964.7115
100	337	153.4485	—	—
100	9	6.2885	47	264.1438
100	5454	2783.0369	—	—
100	102	48.8754	313	1859.7320