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

Table 1

Numerical results of the NEW1 and NEW2.

Number	Prob.	dim	𝑘/nf/ng/𝑡(NEW1); ‖𝑔𝑘‖^2 (NEW1)	𝑘/nf/ng/𝑡(NEW2); ‖𝑔𝑘‖^2 (NEW2)
1	Powell badly scaled	2	6/20/9/0.0010	9/25/11/0.0010
			0.2511	0.2709
2	Brown badly scaled	2	9/26/12/0.0010	9/26/11/0.0010
			0	9.1712𝑒−005
3	Trigonometric function	10	11/48/29/0.0010	13/58/37/0.0020
			0.0056	0.0061
4	Chebyquad	100	30/42/33/0.3594	61/72/65/0.4375
			0.0258	0.0207
5	Penalty function 𝐼	100	5/20/12/0.0313	5/20/12/0.0313
			5.4750𝑒−005	6.8047𝑒−005
		500	11/36/23/0.0010	10/34/20/0.0010
			1.5626𝑒−004	3.9363𝑒−004
6	Allgower	500	4/32/8/0.0156	4/32/8/0.0313
			0.0147	0.0215
7	Variable dimension	500	12/50/14/0.0625	12/50/14/0.0313
			5.9262𝑒−006	5.9262𝑒−006
		1000	16/54/16/0.0313	16/54/16/0.0313
			1.1473𝑒−004	1.1473𝑒−004
5	Penalty function 𝐼	1000	19/44/26/0.0313	22/48/30/0.0156
			0.0010	3.8348𝑒−004
8	Integral equation	1000	2/24/2/0.0010	2/24/2/0.0020
			0.0032	0.0058
9	Separable cubic	1000	9/12/11/0.3594	9/13/11/0.4219
			6.1814𝑒−004	4.0438𝑒−005
		3000	10/14/13/2.5469	9/13/12/2.4063
			7.2599𝑒−005	2.0012𝑒−004