Global Convergence of a Modified Spectral Conjugate Gradient Method

Table 1

Comparison of efficiency with the other methods.

Function	Algorithm	Dim	GV	NI	NF	CT(s)
Rrosenbrock	mfr	2	8.8818𝑒−007	328	7069	0.2970
	prp	2	9.2415𝑒−007	760	41189	1.4370
	mprp	2	8.6092𝑒−007	124	2816	0.0940
	msprp	2	6.9643𝑒−007	122	2597	0.1400
Freudenstein and Roth	mfr	2	5.5723𝑒−007	236	5110	0.2190
	prp	2	7.1422𝑒−007	331	18798	0.6250
	mprp	2	2.4666𝑒−007	67	1904	0.0940
	msprp	2	8.6967𝑒−007	62	1437	0.0780
Brown badly	mfr	2	—	—	—	—
	prp	2	—	—	—	—
	mprp	2	7.9892𝑒−007	105	10279	0.2030
	msprp	2	7.6029𝑒−007	70	7117	0.2660
Beale	mfr	2	6.1730𝑒−007	74	714	0.0780
	prp	2	8.2455𝑒−007	292	12568	0.4370
	mprp	2	6.2257𝑒−007	130	1539	0.0940
	msprp	2	8.7861𝑒−007	91	877	0.0470
Powell singular	mfr	4	9.9827𝑒−007	4122	10578	0.6870
	prp	4	—	—	—	—
	mprp	4	9.6909𝑒−007	13565	218964	5.2660
	msprp	4	9.8512𝑒−007	11893	169537	7.2500
Wood	mfr	4	7.7937𝑒−007	263	5787	0.2660
	prp	4	9.9841𝑒−007	1284	69501	2.3440
	mprp	4	9.6484𝑒−007	280	6432	0.1720
	msprp	4	7.9229𝑒−007	404	9643	0.4070
Extended Powell singular	mfr	4	9.9827𝑒−007	4122	10578	0.6800
	prp	4	—	—	—	—
	mprp	4	9.6909𝑒−007	13565	218964	5.5310
	msprp	4	9.8512𝑒−007	11893	169537	7.4070
Broyden tridiagonal	mfr	4	4.8451𝑒−007	53	784	0.0630
	prp	4	6.6626𝑒−007	87	4460	0.1180
	mprp	4	5.8166𝑒−007	39	430	0.0320
	msprp	4	9.7196𝑒−007	52	785	0.0780