The Global Convergence of a New Mixed Conjugate Gradient Method for Unconstrained Optimization

Table 2

Numerical results of the CGDESCENT and NEW3.

Number	Prob.	dim	𝑘/nf/ng/𝑡(CGDESCENT); ‖𝑔𝑘‖^2 (CGDESCENT)	𝑘/nf/ng/𝑡(NEW3); ‖𝑔𝑘‖^2 (NEW3)
1	Powell badly scaled	2	6/16/7/0.0851	13/38/20/0.0313
			0.2704	0.4305
2	Brown badly scaled	2	13/33/14/0.0010	20/82/44/0.0313
			0	0.9525
3	Trigonometric function	10	12/56/33/0.0010	11/44/27/0.0313
			0.0075	0.0598
4	Chebyquad	100	64/75/67/0.4219	38/58/44/0.2344
			0.0178	0.0175
5	Penalty function 𝐼	100	5/20/12/0.0313	10/37/10/0.0313
			5.4750𝑒−005	3.4737𝑒−004
		500	10/34/20/0.0313	9/27/15/0.0010
			3.8011𝑒−005	2.5130𝑒−004
6	Allgower	500	4/32/8/0.1256	4/32/8/0.1250
			0.0259	0.0089
7	Variable dimension	500	12/50/14/0.0528	12/50/14/0.0313
			5.9262𝑒−006	5.9269𝑒−004
		1000	16/54/16/0.0313	16/53/16/0.0010
			1.1473𝑒−004	5.6730𝑒−005
5	Penalty function 𝐼	1000	22/49/31/0.0313	21/50/30/0.0625
			3.1604𝑒−004	3.4038𝑒−004
8	Integral equation	1000	2/24/2/0.0010	2/24/2/0.0010
			0.0028	0.0156
9	Separable cubic	1000	13/16/14/0.5469	16/20/20/0.5000
			2.5196𝑒−004	2.1274𝑒−004
		3000	10/14/13/2.5469	10/14/13/2.5469
			7.6877𝑒−005	2.2646𝑒−004