[Retracted] Branch-and-Reduction Algorithm for Indefinite Quadratic Programming Problem

Table 1

Numerical comparisons for test examples 1–11.

Examples	Methods	Optimal value	Optimal solution	Iter	Time (s)
1	Ours	10.0000	(2.0000, 8.0000)	59	14.9847
	[12]	10.0000	(2.0000, 8.0000)	56	15.8054
	[20]	10.0000	(2.0000, 8.0000)	41	0.4856
	[21]	10.0000	(2.0000, 8.0000)	27	10.9297
	[22]	10.0000	(2.0000, 8.0000)	53	0.3278
	SCIP solver	10.0000	(2.0000, 8.0000)	1	0.3177
2	Ours	3.00000	(0.0000, 4.0000)	71	16.4324
	[12]	3.00000	(0.0000, 4.0000)	68	17.9814
	[23]	3.00000	(0.0000, 4.0000)	25	2.4936
	SCIP solver	3.00000	(0.0000, 4.0000)	1	0.0678
3	Ours	0.87016	(1.3148, 0.1396, 0.0, 0.4233)	1	0.2889
	[12]	0.87016	(1.3148, 0.1396, 0.0, 0.4233)	1	0.3894
	[22]	0.8902	(1.3148, 0.1396, 0.0, 0.4233)	1	0.5432
	SCIP solver	0.8902	(1.3148, 0.1396, 0.0, 0.4233)	11	0.2912
4	Ours	−16.22662	(0.0, 3.6403, 0.0, 2.9029, 1.9388, 0.0)	1	0.5949
	[12]	−16.22662	(0.0, 3.6403, 0.0, 2.9029, 1.9388, 0.0)	1	0.7498
	SCIP solver	−16.2266	(0.0, 3.6403, 0.0, 2.9029, 1.9388, 0.0)	1	0.0882
5	Ours	−3.00000	(3.0000, 3.0000)	32	6.2275
	[12]	−3.00000	(3.0000, 3.0000)	30	6.3380
	SCIP solver	−3.00000	(3.0000, 3.0000)	5	0.2438
6	Ours	−1.06250	(0.7500, 2.0000)	2	0.4150
	[12]	−1.06250	(0.7500, 2.0000)	2	0.5638
	SCIP solver	−1.0625	(0.7500, 2.0000)	1	0.1129
7	Ours	10	(2, 8)	18	4.5829
	[26]	10	(2, 8)	3	0.6745
	SCIP solver	10	(2, 8)	1	0.0369
8	Ours	4	(0, 0)	1	0.2276
	[26]	4	(0, 0)	2	0.4219
	SCIP solver	4	(0, 0)	1	0.1203
9	Ours	−4558	(27, 20)	35	7.4568
	SCIP solver	−4558	(27, 20)	1	0.0359
10	Ours	2.39991	(0.5828, 0.6969, 0.7515, 0.2685)	1	0.5809
	SCIP solver	2.39991	(0.5828, 0.6969, 0.7515, 0.2685)	11	0.6186
11	Ours	6.96376	(0.7767, 0.7497, 0.9079, 0.0532)	1	0.5354
	SCIP solver	6.96376	(0.7767, 0.7497, 0.9079, 0.0532)	14	0.6093