Primal-dual interior point QP-free algorithm for nonlinear constrained optimization

Jian, Jinbao; Zeng, Hanjun; Ma, Guodong; Zhu, Zhibin

doi:10.1186/s13660-017-1500-2

Journal of Inequalities and Applications

Table 2 Numerical experiment compared reports

From: Primal-dual interior point QP-free algorithm for nonlinear constrained optimization

Prob.	n	\(\boldsymbol{m_{e}}\)	\(\boldsymbol{m_{i}}\)	Algorithm A in this paper						Algorithm from [ 1 ]
Prob.	n	\(\boldsymbol{m_{e}}\)	\(\boldsymbol{m_{i}}\)	Itr	Nf	N	\(\boldsymbol{\bar{\rho}}\)	\(\boldsymbol{f_{\mathrm{final}}}\)	Tcpu	Itr	\(\boldsymbol{\bar{\rho }}\)	\(\boldsymbol{f_{\mathrm{final}}}\)
HS1	2	0	1	28	73	70	1	1.7825e − 18	0.02	24	1	6.5782e − 27
HS3	2	0	1	6	7	8	1	2.3501e − 06	0.01	4	1	8.5023e − 09
HS4	2	0	2	7	13	29	1	2.6667e + 00	0.01	4	1	2.6667e + 00
HS5	2	0	4	5	13	47	1	−1.9132e + 00	0.01	6	1	−1.9132e + 00
HS6	2	1	0	9	364	718	1	2.4199e − 07	0.03	7	2	0.0000e + 00
HS7	2	1	0	8	15	28	32	−1.7320e + 00	0.01	9	2	−1.7321e + 00
HS8	2	2	0	9	16	59	8,192	−1.0000e + 00	0.01	14	1	−1.0000e + 00
HS9	2	1	0	18	34	66	8,192	−4.9985e − 01	0.02	10	1	−5.0000e + 01
HS12	2	0	1	9	19	39	1	−3.0000e + 01	0.01	5	1	−3.0000e + 01
HS24	2	0	5	16	29	179	1	−1.0000e + 00	0.02	14	1	−1.0000e + 00
HS25	3	0	6	1	1	6	1	9.4934e − 31	0.01	62	1	1.8185e − 16
HS26	3	1	0	16	76	142	2	1.6085e − 04	0.02	19	2	2.8430e − 12
HS27	3	1	0	28	484	939	4	3.9958e − 02	0.05	14	32	4.0000e − 02
HS28	3	1	0	11	38	71	1,024	7.5674e − 08	0.01	6	1	0.0000e + 00
HS29	3	0	1	11	24	53	1	−2.2627e + 01	0.01	8	1	−2.2627e + 01
HS30	3	0	7	7	10	63	1	1.0000e + 00	0.02	7	1	1.0000e + 00
HS32	3	1	4	19	33	166	128	9.8818e − 01	0.02	24	4	1.0000e + 00
HS33	3	0	6	15	20	189	1	−4.5178e + 00	0.02	29	1	−4.5858e + 00
HS34	3	0	8	10	15	104	1	−8.3403e − 01	0.02	30	1	−0.8340e + 00
HS36	3	0	7	10	15	144	1	−3.3000e + 03	0.02	10	1	−3.3000e + 03
HS37	3	0	8	12	19	200	1	−3.4560e + 03	0.02	7	1	−3.4560e + 03
HS38	4	0	8	73	153	1,218	1	1.9761e − 11	0.06	37	1	3.1594e − 24
HS39	4	2	0	11	19	63	1	2.5328e − 04	0.02	19	4	−1.0000e + 00
HS40	4	3	0	49	108	726	2	−2.5000e − 01	0.05	4	2	−2.500e + 00
HS42	4	2	0	36	70	290	1,024	1.3883e + 01	0.03	6	4	1.3858e + 01
HS43	4	0	3	12	29	73	1	−4.4000e + 01	0.02	9	1	−4.4000e + 01
HS46	5	2	0	101	234	735	1	1.3088e − 04	0.05	25	2	6.6616e − 12
HS47	5	3	0	21	54	276	1	2.0468e − 04	0.04	25	16	8.0322e − 14
HS48	5	2	0	21	55	202	2,048	3.1361e − 09	0.02	6	4	0.0000e + 00
HS49	5	2	0	51	87	276	64	1.1761e − 02	0.03	69	64	3.5161e − 12
HS50	5	3	0	50	200	1,065	128	9.3190e − 05	0.04	11	512	4.0725e − 17
HS51	5	3	0	29	132	722	256	2.2808e − 05	0.03	8	4	0.0000e + 00
HS52	5	3	0	31	45	225	256	5.2930e + 00	0.03	4	8	5.3266e + 00
HS53	5	3	10	36	69	1,694	256	4.0734e + 00	0.06	5	8	4.0930e + 00
HS56	7	4	0	21	43	2,482	4	−2.6183e + 00	0.06	12	4	−3.4560e + 00
HS57	2	0	3	34	53	141	1	2.8461e − 02	0.03	15	18	2.8460e − 02
HS60	3	1	6	18	43	574	1	3.2650e − 02	0.04	7	1	3.2568e − 02
HS61	3	2	0	16	255	986	256	−1.7195e + 02	0.03	44	128	−1.4365e + 02
HS62	3	1	6	8	19	153	1	−2.6273e + 04	0.02	5	1	−2.6273e + 04
HS63	3	2	3	15	27	200	1	9.6232e + 02	0.02	5	2	9.6172e + 02
HS66	3	0	8	15	42	249	1	5.1816e − 01	0.02	1,000⁺	1	5.1817e − 01
HS70	4	0	9	16	22	214	1	1.0085e − 02	0.03	22	1	1.7981e − 01
HS73	4	1	6	17	35	213	1	2.9896e + 01	0.03	16	1	2.9894e + 01
HS77	5	2	0	21	141	587	1	4.5981e − 01	0.06	13	1	2.4151e − 01
HS78	5	3	0	23	66	329	1	−2.9197e + 00	0.03	4	4	−2.9197e + 00
HS79	5	3	0	16	26	123	128	7.8681e − 02	0.02	7	2	7.8777e − 02
HS80	5	3	10	66	196	3,975	4	6.0149e − 02	0.14	6	2	5.3950e − 02
HS81	5	3	10	19	37	708	8	6.4109e − 02	0.05	9	8	5.3950e − 02
HS84	5	0	16	30	57	1,252	1	−5.2803e + 06	0.06	30	1	−5.2803e + 06
HS93	6	0	8	21	43	1,387	1	1.3629e + 02	0.04	12	1	1.3508e + 02
HS99	7	2	14	18	31	57	1	−8.3108e + 08	0.02	8	4	0.0000e + 00
HS100	7	0	4	8	22	86	1	6.8063e + 02	0.02	9	1	6.8063e + 02
HS107	9	6	8	41	67	1,086	1	1.3748e − 08	0.06	1,000⁺	8,192	5.0545e + 38
HS110	10	0	20	11	510	10,146	1	−4.3134e + 01	0.13	6	1	−4.5778e + 01
HS111	10	3	20	26	264	6,542	1,024	−5.8531e + 01	0.14	1,000⁺	1	−4.7760e + 01
HS112	10	3	10	6	11	199	2	−5.3197e + 01	0.02	11	1	−4.7761e + 01
HS113	10	0	8	21	48	519	1	2.4306e + 01	0.03	10	1	2.4306e + 01
HS114	10	3	28	11	136	4,474	16	−1.3407e + 03	0.13	39	256	−1.7688e + 03
HS118	15	0	59	34	51	2,554	1	6.6482e + 02	0.12	-	-	-

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