A Novel Self-Adaptive Trust Region Algorithm for Unconstrained Optimization

Table 1

Numerical comparisons of BTR, RATR, ΛATR, and LATR.

Problem	Dim	BTR		RATR		ΛATR		LATR
		nf	ng	nf	ng	nf	ng	nf	ng
(1) Trigonometric	200	214	17	205	10	—	—	78	9
(2) Extended Powell singular	200	28	20	26	20	32	21	30	24
(3) Schittkowski function 302	200	239	160	363	275	117	24	83	65
(4) Linear function full rank	200	23	4	21	4	15	3	11	7
(5) Watson	200	30	14	22	10	16	10	18	11
	300	39	15	115	78	73	49	67	48
	400	84	39	27	12	38	25	107	78
	500	95	43	29	14	68	48	39	26
(6) Nearly separable	200	41	21	27	15	23	16	24	17
	300	46	25	34	18	24	16	23	16
	400	52	25	39	23	33	22	26	19
	500	—	—	—	—	—	—	37	26
(7) Yang tridiagonal	200	67	40	61	44	99	32	51	41
	300	151	113	72	57	105	38	74	61
	400	133	93	141	106	151	68	109	90
	500	148	97	120	95	257	149	109	90
(8) Allgower	200	40	23	53	38	57	2	83	69
	300	18	1	17	1	24	1	7	1
	400	25	15	17	3	56	2	21	17
	500	20	3	17	3	52	3	9	2
(9) Linear function rank 1	200	101	42	62	27	285	30	39	24
	300	102	40	66	25	300	30	35	16
	400	110	45	69	25	319	32	39	20
	500	108	42	70	25	317	31	47	32
(10) Linear function rank 1 with zero columns and rows	200	64	3	60	2	21	2	22	2
	300	67	3	64	3	21	1	21	1
	400	66	1	65	1	29	5	22	1
	500	78	6	67	2	24	2	26	4
(11) Discrete integral equation	200	54	19	24	4	39	14	27	18
	300	31	5	70	46	42	22	30	28
	400	44	12	43	32	32	16	31	29
	500	49	15	37	17	45	23	31	29
(12) CRAGGLVY	200	36	9	35	9	22	10	19	9
(13) GENHUMPS	200	26	0	26	0	74	0	9	0
(14) BROYDNBD	200	32	7	20	14	47	0	17	15
(15) PENALTY	200	71	33	69	33	59	33	59	37
	300	75	35	74	35	63	38	59	35
	400	74	33	76	35	64	36	61	37
	500	77	35	80	37	58	36	62	38
(16) PENALTY2	200	46	8	42	8	88	9	25	11
	300	149	72	159	129	78	50	150	116
	400	434	208	—	—	—	—	465	390
	500	—	—	330	228	—	—	—	—
(17) CHEBYQAD	200	75	55	79	70	39	7	83	67
	300	28	12	83	70	41	6	89	70
	400	95	63	99	85	108	64	104	82
	500	32	16	37	22	119	52	103	83
(18) GENROSE	200	194	161	253	248	265	172	241	205
	300	308	235	381	373	394	248	357	303
	400	405	301	487	479	499	323	468	399
	500	—	—	—	—	—	—	—	—
(19) INTEGREQ	200	15	1	14	1	214	0	6	1
	300	15	1	14	1	206	0	6	1
	400	15	1	14	1	203	0	6	1
	500	15	1	14	1	201	0	6	1
(20) FLETCHCR	200	113	88	151	146	157	91	158	132
	300	147	122	218	213	224	132	233	195
	400	183	157	292	284	295	175	309	258
	500	217	190	357	351	362	211	384	321
(21) ARGLINB	200	6	5	6	5	6	5	6	5
	300	7	6	7	6	7	6	7	6
	400	7	6	7	6	300	5	7	6
	500	7	6	7	6	424	5	7	6
(22) NONDIA	200	7	6	7	6	93	6	7	6
	300	7	6	7	6	7	6	7	6
	400	6	5	6	5	6	5	6	5
	500	6	5	6	5	6	5	6	5
(23) EG2	200	14	9	11	9	59	23	10	8
	300	14	9	12	9	60	27	6	5
	400	9	7	7	6	180	30	8	6
	500	12	5	17	13	111	34	14	11
(24) CURLY20	200	13	11	19	17	16	14	11	10
	300	13	11	21	18	17	15	13	12
	400	10	9	11	11	11	10	9	9
	500	10	9	11	11	11	10	9	9
(25) CUBE	200	52	20	39	25	95	16	37	29
	300	50	16	77	65	98	20	40	32
	400	52	16	45	31	83	16	35	28
	500	52	16	52	38	128	14	35	28
(26) EXPLIN1	200	30	2	28	2	12	3	13	4
	300	29	1	28	1	33	4	13	4
	400	31	2	29	2	23	4	21	16
	500	32	2	30	2	15	3	13	4
(27) SINQUAD	200	68	55	18	17	119	14	19	17
	300	186	175	16	15	225	20	64	60
	400	25	12	21	19	224	25	48	45
	500	31	15	43	41	229	40	35	33
(28) LIARWHD	200	29	1	28	1	50	2	14	4
	300	32	2	29	2	18	2	12	2
	400	30	1	30	1	30	2	12	1
	500	30	1	30	1	33	2	11	1

— means that the algorithm reaches 500 iterations.