New cautious BFGS algorithm based on modified Armijo-type line search

Journal of Inequalities and Applications

Table 1 Comparison of efficiency with other method

Functions	Algorithm	*Dim*	GV	NI	NF	CT
Rosenbrock	CBFGS	2	6.2782e-007	35	74	0.0310s
Rosenbrock	NCBFGS	2	1.1028e-007	40	70	0.0310s
Freudenstein and Roth	CBFGS	2	7.9817e-007	28	82	0.0310s
Freudenstein and Roth	NCBFGS	2	2.7179e-007	11	25	0.0320s
Beale	CBFGS	2	7.2275e-007	40	55	0.0310s
Beale	NCBFGS	2	3.1136e-007	18	23	0.0470s
Brown badly	CBFGS	2	7.7272e-007	36	223	0.0310s
Brown badly	NCBFGS	2	0	29	50	0.0620s
Broyden tridiagonal	CBFGS	4	7.5723e-007	26	126	0.0320s
Broyden tridiagonal	NCBFGS	4	3.8712e-007	15	21	0.0310s
Powell singular	CBFGS	4	9.9993e-007	13,993	14,031	2.4530s
Powell singular	NCBFGS	4	9.4607e-007	31	38	0.0320s
Kowalik and Osborne	CBFGS	4	9.9783e-007	3126	3128	2.1250s
Kowalik and Osborne	NCBFGS	4	4.4454e-007	30	45	0.0470s
Brown almost-linear	CBFGS	6	9.5864e-007	263	300	0.1100s
Brown almost-linear	NCBFGS	6	1.2290e-007	22	30	0.0160s
Discrete boundary	CBFGS	6	8.6773e-007	79	85	0.0470s
Discrete boundary	NCBFGS	6	3.3650e-007	14	17	0.0320s
Variably dimensioned	CBFGS	8	3.4688e-008	7	51	0.0470s
Variably dimensioned	NCBFGS	8	3.1482e-007	10	21	0.0320s
Extended Rosenbrock	CBFGS	8	8.2943e-007	91	190	0.0470s
Extended Rosenbrock	NCBFGS	8	7.7959e-007	99	149	0.0320s
Extended Powell singular	CBFGS	8	9.9975e-007	6154	6199	1.4690s
Extended Powell singular	NCBFGS	8	6.5685e-007	42	55	0.0630s
Brown almost-linear	CBFGS	8	9.8392e-007	364	379	0.1880s
Brown almost-linear	NCBFGS	8	4.8080e-007	20	27	0.0780s
Broyden tridiagonal	CBFGS	9	4.4261e-007	38	86	0.0470s
Broyden tridiagonal	NCBFGS	9	6.2059e-007	41	56	0.0310s
Linear-rank1	CBFGS	10	-	-	-	-
Linear-rank1	NCBFGS	10	2.6592e-007	4	15	0.0310s
Linear-full rank	CBFGS	12	9.5231e-007	18	36	0.0160s
Linear-full rank	NCBFGS	12	9.4206e-016	2	3	0.0150s