A Fractional Trust Region Method for Linear Equality Constrained Optimization

Table 2

The numerical results of Algorithm 7 for some test problems.

Pro.		Starting point	Algorithm	Iter	nf/ng		CPU (s)
1	6	(0, 0, 0, 0, 0, 0)	CTR	6	7/8	7.559746(−5)	0.084639
			FTR	5	6/6	1.693174(−5)	0.161438
2	5	(3, 5, −3, 2, −2)	CTR	13	14/9	1.637781(−5)	0.094287
			FTR	8	9/9	2.148387(−6)	0.098268
3	5	(2, 2, −9, 3, 3)	CTR	27	28/21	5.815109(−5)	0.110429
			FTR	25	26/17	4.996278(−5)	0.149000
4	10	(0, −6, 6, 0, 0,	CTR	12	13/13	3.889891(−5)	0.100359
		0, −6, 6, 0, 0)	FTR	8	9/9	2.397640(−5)	0.152117
5	8	(0, 3, −1, −2	CTR	16	17/14	7.255223(−5)	0.099120
		0, 3, −1, −2)	FTR	16	17/17	1.249467(−5)	0.129272
6	8	(7/3, 11/3, −1, −1	CTR	22	23/19	3.128858(−6)	0.101571
		7/3, 11/3, −1, −1)	FTR	21	22/19	2.865070(−7)	0.167233
7	6	(3, 4, 3, 4, 3, 4)	CTR	8	9/9	2.208537(−7)	0.093060
			FTR	8	9/9	1.765690(−8)	0.139521
8	6	(3, 4, 3, 4, 3, 4)	CTR	14	15/11	8.493218(−7)	0.095873
			FTR	12	13/10	1.155176(−5)	0.166608
9	6	(6, 8, 6, 8, 6, 8)	CTR	21	22/18	1.208648(−6)	0.094048
			FTR	19	20/18	3.705893(−5)	0.170549
10	6	−(1.5, 2, 1.5, 2, 1.5, 2)	CTR	13	14/10	1.789828(−6)	0.104145
			FTR	9	10/7	4.017095(−6)	0.158877
11	8	(0.3, 0.4, …, 0.3, 0.4)	CTR	15	16/13	3.013621(−5)	0.087370
			FTR	7	8/8	7.252083(−5)	0.121116
12	6	(0.3, 0.4, …, 0.3, 0.4)	CTR	26	27/16	5.317180(−5)	0.1160001
			FTR	24	25/14	5.917188(−5)	0.187447
13	6	(1.5, 2, 1.5, 2, 1.5, 2)	CTR	6	7/7	8.707409(−5)	0.081667
			FTR	6	7/7	5.998420(−5)	0.115520
14	6	(6, 8, 6, 8, 6, 8)	CTR	34	35/20	3.185767(−5)	0.106515
			FTR	22	23/23	4.845919(−6)	0.158603
15	8	(0.3, 0.4, …, 0.3, 0.4)	CTR	10	11/9	1.738762(−5)	0.092062
			FTR	9	10/8	5.005195(−5)	0.146342
16	6	(0.3, 0.4, …, 0.3, 0.4)	CTR	13	14/12	3.409181(−5)	0.083445
			FTR	12	13/12	9.332787(−5)	0.164178
17	6	(0.3, 0.4, …, 0.3, 0.4)	CTR	29	30/17	1.845528(−6)	0.088997
			FTR	19	20/17	5.983264(−6)	0.159851
18	8	(0.3, 0.4, …, 0.3, 0.4)	CTR	12	13/9	7.722466(−7)	0.087020
			FTR	9	10/9	4.353866(−7)	0.149733