Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 3 Numerical results of Example 4

From: On q-BFGS algorithm for unconstrained optimization problems

Starting point	q-BFGS algorithm
Starting point	it	fe	ge	\(x^{*}\)	\(f(x^{*})\)
\((4 , 3)^{T}\)	31	199	33	\((1.047, 1.088)^{T}\)	0.0112
\((-3, 1)^{T}\)	13	98	16	\((0.914, 0.852)^{T}\)	0.013401
\((-1, 3)^{T}\)	28	179	32	\((1.016, 1.018)^{T}\)	0.009
\((-1.5, 3.7)^{T}\)	24	158	29	\((0.879 , 0.753)^{T}\)	0.007
\((-1 , 4)^{T}\)	19	123	19	\((0.967 , 0.939)^{T}\)	2.39e − 03
\((1, -1)^{T}\)	16	122	18	\((1.037 , 1.066)^{T}\)	0.010
\((-4, 2)^{T}\)	23	151	27	\((0.928 , 0.869)^{T}\)	0.000
\((-1, -4)^{T}\)	17	116	18	\((0.830 , 0.691)^{T}\)	0.015
\((-2, 2)^{T}\)	16	113	19	\((0.721 , 0.496)^{T}\)	0.001
\((-5, 6)^{T}\)	27	178	31	\((0.908 , 0.823)^{T}\)	0.006
\((-3, 6)^{T}\)	32	199	36	\((0.975 , 0.948)^{T}\)	0.002
\((4, -5)^{T}\)	18	125	21	\((0.859 , 0.721)^{T}\)	0.003
\((4, -7)^{T}\)	20	142	22	\((1.046 , 1.084)^{T}\)	0.011
\((-5, -3)^{T}\)	14	111	16	\((0.949 , 0.897)^{T}\)	0.005
\((4, -5.6)^{T}\)	14	109	16	\((0.976 , 0.959)^{T}\)	0.004
\((-8, 2)^{T}\)	3	41	4	\((1.000 , 2.563)^{T}\)	0.008
\((-5, 7)^{T}\)	26	165	27	\((0.991 , 0.964)^{T}\)	0.006
\((-2, 6)^{T}\)	33	199	37	\((0.975 , 0.941)^{T}\)	0.008
\((1, -5)^{T}\)	19	152	20	\((1.057 , 1.113)^{T}\)	0.014
\((-3, -4)^{T}\)	16	115	17	\((0.933 , 0.873)^{T}\)	0.000
\((8, 1)^{T}\)	21	149	27	\((0.723 , 0.499)^{T}\)	0.000
\((3, -7)^{T}\)	12	90	13	\((0.885 , 0.789)^{T}\)	0.006
\((4, -5)^{T}\)	18	125	21	\((0.859 , 0.721)^{T}\)	0.003
\((-5, -2)^{T}\)	17	117	18	\((0.940 , 0.886)^{T}\)	0.002
\((4, -6)^{T}\)	16	119	19	\((1.119 , 1.238)^{T}\)	0.012
\((3, -4)^{T}\)	12	96	13	\((0.993 , 0.978)^{T}\)	0.003
\((4, -4)^{T}\)	15	108	16	\((0.815 ,0.6813)^{T}\)	0.011

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