Use an interface instead of accessing internal fields

[blegat]

The idea is to split separate the details about the problem representation with the optimization algorithm. It should make it easier to add support for low-rank matrices after this refactoring.

• Regression on control7 of SDPLib
• maxG11 rank1 of SDPLib Add low-rank Ai support for Schur complement blegat/LowRankOpt.jl#75

Current benchmark on SDPLIB

Benchmark added in #30

problem	n	m	main (s)	nlpmodel (s)	speedup	it main	it nlpmodel	obj main	obj nlpmodel
gpp250-1	250	250	1.546	1.411	1.10×	22	18	80800.6	-15.4449
hinf1	14	13	0.002	0.002	1.11×	24	23	2.03266	2.03265
mcp124-3	124	124	0.066	0.059	1.12×	11	11	467.75	467.75
mcp124-4	124	124	0.067	0.058	1.15×	11	11	864.412	864.412
theta1	50	104	0.019	0.017	1.16×	11	11	23	23
qap8	65	529	0.506	0.432	1.17×	20	15	1.54015e+10	2052.57
qap7	50	358	0.209	0.172	1.22×	18	17	5.16172e+10	1076.81
mcp500-2	500	500	4.038	3.313	1.22×	13	13	1070.06	1070.06
truss1	13	6	0.001	0.001	1.28×	11	11	-9	-9
hinf3	16	13	0.003	0.002	1.29×	28	29	56.948	56.9485
hinf4	16	13	0.003	0.002	1.29×	30	29	274.764	274.765
theta3	150	1106	3.754	2.898	1.30×	13	13	42.167	42.167
infd2	30	10	0.013	0.009	1.34×	24	24	-1.26218e+57	-1.26212e+57
truss5	331	208	0.180	0.131	1.37×	16	16	-132.636	-132.636
equalG11	801	801	21.860	15.619	1.40×	13	13	629.155	629.155
hinf15	37	91	0.027	0.019	1.41×	27	27	20.2773	24.442
hinf10	18	21	0.004	0.003	1.46×	33	30	108.817	108.866
truss4	19	12	0.001	0.001	1.54×	11	11	-9.01	-9.01
hinf12	24	43	0.027	0.018	1.55×	101	101	1.15236e-08	9.9035e-09
control2	30	66	0.018	0.012	1.56×	25	25	8.3	8.3
hinf14	34	73	0.016	0.010	1.57×	22	21	13.0007	12.9974
hinf8	16	13	0.003	0.002	1.59×	28	23	116.359	116.213
mcp250-2	250	250	0.815	0.471	1.73×	11	11	531.93	531.93
mcp500-3	500	500	5.426	3.072	1.77×	12	12	1847.97	1847.97
control3	45	136	0.081	0.046	1.77×	26	25	13.6333	13.6333
maxG11	800	800	24.032	13.527	1.78×	13	13	629.165	629.165
gpp500-4	500	501	6.593	3.686	1.79×	12	13	-1567.02	-1567.02
truss8	628	496	3.361	1.823	1.84×	17	17	-133.115	-133.115
mcp500-4	500	500	5.743	3.111	1.85×	12	12	3566.74	3566.74
theta4	200	1949	24.027	12.864	1.87×	14	14	50.3212	50.3212
gpp500-1	500	501	14.222	7.569	1.88×	25	26	9.73956e+06	-25.3205
control9	135	1081	14.264	7.492	1.90×	34	34	14.6754	14.6754
mcp250-1	250	250	0.968	0.502	1.93×	12	12	317.264	317.264
qap9	82	748	2.295	1.089	2.11×	16	17	5.2357e+10	-348.686
mcp500-1	500	500	7.657	3.493	2.19×	14	14	598.149	598.149
arch2	335	174	1.902	0.858	2.22×	20	20	0.671516	0.671516
qap10	101	1021	4.408	1.948	2.26×	18	16	2860.67	7118.68
arch8	335	174	1.908	0.840	2.27×	20	20	7.05698	7.05698
ss30	426	132	8.680	3.541	2.45×	20	20	20.2395	20.2395
theta2	100	498	0.917	0.366	2.51×	12	12	32.8792	32.8792
mcp250-4	250	250	1.180	0.458	2.57×	11	11	1681.96	1681.96
hinf13	30	57	0.020	0.008	2.59×	24	24	44.8958	45.1178
mcp100	100	100	0.093	0.035	2.64×	11	11	226.157	226.157
mcp250-3	250	250	1.204	0.453	2.66×	11	11	981.173	981.173
control1	15	21	0.006	0.002	2.67×	24	24	17.7846	17.7846
arch4	335	174	2.267	0.849	2.67×	20	20	0.972628	0.972628
arch0	335	174	2.494	0.933	2.67×	22	22	0.566517	0.566517
hinf5	16	13	0.006	0.002	2.74×	25	29	362.92	362.913
hinf11	22	31	0.012	0.004	2.74×	33	34	65.9106	65.9138
control6	90	496	3.443	1.170	2.94×	40	39	37.3045	37.3044
hinf6	16	13	0.007	0.002	2.97×	32	31	449.011	448.941
gpp250-3	250	250	2.051	0.680	3.02×	20	15	-303.539	-303.539
gpp500-2	500	501	12.746	4.097	3.11×	22	15	122387	-156.06
qap6	37	229	0.196	0.062	3.17×	23	17	113.203	3047.57
truss2	133	58	0.039	0.012	3.17×	15	15	-123.38	-123.38
control8	120	861	14.320	4.455	3.21×	35	35	20.2864	20.2864
infp1	30	10	0.030	0.009	3.29×	28	23	4.81296	5.18035
hinf9	16	13	0.007	0.002	3.31×	33	27	236.249	236.249
infd1	30	10	0.041	0.012	3.33×	31	31	-1.42829e+58	-1.42825e+58
gpp124-1	124	125	0.620	0.184	3.36×	43	30	-7.34307	66.5973
control7	105	666	9.277	2.749	3.37×	39	39	20.6251	20.6251
control5	75	351	1.569	0.464	3.38×	36	33	16.8836	16.8836
gpp500-3	500	501	13.250	3.840	3.45×	23	14	3.41937e+08	-513.018
infp2	30	10	0.033	0.009	3.64×	28	23	7.33315	4.54581
qap5	26	136	0.041	0.011	3.68×	15	10	2.883e+12	-436
hinf7	16	13	0.007	0.002	3.73×	34	24	392.315	390.816
hinf2	16	13	0.007	0.002	3.78×	34	24	10.9699	10.9671
gpp250-2	250	250	2.336	0.563	4.15×	23	12	1188.17	-81.869
control4	60	231	0.642	0.149	4.30×	35	27	19.7942	19.7942
truss7	301	86	0.243	0.052	4.69×	27	25	-900.001	-900.001
gpp124-2	124	125	0.585	0.122	4.80×	28	20	902.828	-46.8623
gpp124-4	124	125	0.502	0.086	5.84×	36	14	-261.092	-418.988
truss3	31	27	0.011	0.002	5.93×	11	11	-9.10999	-9.10999
mcp124-2	124	124	0.378	0.063	6.02×	12	12	269.88	269.88
mcp124-1	124	124	0.458	0.068	6.74×	12	12	141.99	141.99
gpp124-3	124	125	0.502	0.073	6.88×	35	12	5.03715e+06	-153.014
truss6	451	172	0.824	0.080	10.31×	24	23	-901.001	-901.001
gpp100	100	101	0.587	0.043	13.59×	64	12	9.86352e+08	-44.9435
control10	150	1326	—	15.809	—	—	38	—	38.5331
control11	165	1596	—	31.997	—	—	42	—	31.9587
gpp250-4	250	250	—	0.612	—	—	14	—	-747.328
thetaG11	801	2401	—	—	—	—	—	—	—
maxG51	1000	1000	—	32.057	—	—	14	—	4006.26

82 problems solved by both — total time: 469.847s (main) vs 420.566s (nlpmodel); overall 1.12×, geometric-mean per-problem 1.24×.