混合优化算法（optimtool.hybrid）

import optimtool as oo
from optimtool.base import np, sp, plt

pip install optimtool>=2.5.0

混合优化算法（optimtool.hybrid）

import optimtool.hybrid as oh
oh.[方法名].[函数名]([目标函数], [参数表], [初始迭代点], [正则化参数], [邻近算子名])

$$\varphi (x)=f(x)+h(x)$$
其中$f(x)$是可微的。$h(x)$不是可微的，并且具备简单的形式。optimtool.hybrid能够选择的$h(x)$有：$||x|{|}_1$, $||x|{|}_2$, $-{\sum }_i\ln (x_i)$，实例：
$$f(x)=\sum _{i=1}^n((n-\sum _{j=1}^n\cos x_j)+i(1-\cos x_i)-\sin x_i{)}^2,x_0=[0.2,0.2,...,0.2]$$

import optimtool.hybrid as oh
x = sp.symbols("x1:3")
f = (2 - (sp.cos(x[0]) + sp.cos(x[1])) + (1 - sp.cos(x[0])) - sp.sin(x[0]))**2 + \
    (2 - (sp.cos(x[0]) + sp.cos(x[1])) + 2 * (1 - sp.cos(x[1])) - sp.sin(x[1]))**2
x_0 = (0.2, 0.2) # Random given

近似点算法（approt）

oh.approt.[函数名]([目标函数], [参数表], [初始迭代点], [正则化参数], [邻近算子名])

方法头	解释
grad(funcs: FuncArray, args: ArgArray, x_0: PointArray, mu: float=1e-3, proxim: str=“L1”, tk: float=0.02, verbose: bool=False, draw: bool=True, output_f: bool=False, epsilon: float=1e-6, k: int=0) -> OutputType	基于梯度方法的邻近近似

oh.approt.grad(f, x, x_0, verbose=True, epsilon=1e-4)

(0.2, 0.2)	0.033830304000793295	0
[0.19925643 0.19925643]	0.03371630105707655	1
[0.19849759 0.19849759]	0.033599113758384015	2
[0.19772323 0.19772323]	0.0334786576252087	3
[0.19693311 0.19693311]	0.03335484671764522	4
[0.19612697 0.19612697]	0.03322759368760871	5
[0.19530458 0.19530458]	0.03309680983956681	6
[0.19446568 0.19446568]	0.032962405200405005	7
[0.19361004 0.19361004]	0.03282428859906577	8
[0.19273741 0.19273741]	0.03268236775663266	9
[0.19184754 0.19184754]	0.03253654938754205	10
[0.19094021 0.19094021]	0.03238673931263206	11
[0.19001517 0.19001517]	0.03223284258474419	12
[0.18907219 0.18907219]	0.032074763627614224	13
[0.18811105 0.18811105]	0.031912406388790386	14
[0.18713151 0.18713151]	0.03174567450732931	15
[0.18613337 0.18613337]	0.03157447149700892	16
[0.1851164 0.1851164]	0.03139870094579865	17
[0.18408039 0.18408039]	0.031218266732314086	18
[0.18302515 0.18302515]	0.03103307325995774	19
[0.18195048 0.18195048]	0.03084302570942143	20
[0.18085618 0.18085618]	0.030648030310189818	21
[0.17974209 0.17974209]	0.03044799463163445	22
[0.17860802 0.17860802]	0.030242827894225312	23
[0.17745382 0.17745382]	0.030032441301325655	24
[0.17627935 0.17627935]	0.029816748391938645	25
[0.17508445 0.17508445]	0.029595665414685356	26
[0.17386901 0.17386901]	0.029369111723178076	27
[0.17263291 0.17263291]	0.029137010192819283	28
[0.17137605 0.17137605]	0.028899287658918093	29
[0.17009835 0.17009835]	0.028655875375845567	30
[0.16879974 0.16879974]	0.02840670949677072	31
[0.16748017 0.16748017]	0.02815173157332011	32
[0.1661396 0.1661396]	0.02789088907428339	33
[0.16477802 0.16477802]	0.027624135922245694	34
[0.16339543 0.16339543]	0.02735143304677512	35
[0.16199186 0.16199186]	0.02707274895251694	36
[0.16056734 0.16056734]	0.026788060300246677	37
[0.15912196 0.15912196]	0.026497352498637897	38
[0.15765579 0.15765579]	0.02620062030415762	39
[0.15616897 0.15616897]	0.025897868426188044	40
[0.15466162 0.15466162]	0.02558911213410671	41
[0.15313393 0.15313393]	0.025274377862715594	42
[0.15158608 0.15158608]	0.024953703812053064	43
[0.15001829 0.15001829]	0.024627140537261723	44
[0.14843083 0.14843083]	0.02429475152384472	45
[0.14682398 0.14682398]	0.023956613743302973	46
[0.14519804 0.14519804]	0.023612818183825806	47
[0.14355337 0.14355337]	0.023263470350419237	48
[0.14189035 0.14189035]	0.02290869072858788	49
[0.14020939 0.14020939]	0.022548615205470916	50
[0.13851092 0.13851092]	0.022183395442150533	51
[0.13679544 0.13679544]	0.02181319919073435	52
[0.13506345 0.13506345]	0.021438210549756025	53
[0.13331551 0.13331551]	0.021058630151454174	54
[0.13155219 0.13155219]	0.020674675274577677	55
[0.12977412 0.12977412]	0.02028657987655194	56
[0.12798195 0.12798195]	0.01989459453910834	57
[0.12617636 0.12617636]	0.019498986321851795	58
[0.12435809 0.12435809]	0.01910003851871226	59
[0.12252788 0.12252788]	0.01869805031281132	60
[0.12068653 0.12068653]	0.01829333632594862	61
[0.11883487 0.11883487]	0.01788622605971978	62
[0.11697374 0.11697374]	0.01747706322615784	63
[0.11510403 0.11510403]	0.017066204966793598	64
[0.11322666 0.11322666]	0.016654020960107936	65
[0.11134258 0.11134258]	0.016240892418513574	66
[0.10945276 0.10945276]	0.01582721097723825	67
[0.10755818 0.10755818]	0.015413377478760959	68
[0.10565989 0.10565989]	0.01499980065777625	69
[0.10375891 0.10375891]	0.014586895732992659	70
[0.1018563 0.1018563]	0.014175082913403667	71
[0.09995316 0.09995316]	0.013764785827967332	72
[0.09805056 0.09805056]	0.013356429888878502	73
[0.09614962 0.09614962]	0.012950440599784873	74
[0.09425145 0.09425145]	0.01254724182137033	75
[0.09235718 0.09235718]	0.012147254007661526	76
[0.09046792 0.09046792]	0.011750892427213808	77
[0.08858482 0.08858482]	0.011358565383947966	78
[0.08670899 0.08670899]	0.01097067245284757	79
[0.08484156 0.08484156]	0.010587602745955627	80
[0.08298365 0.08298365]	0.010209733224125174	81
[0.08113635 0.08113635]	0.009837427069776122	82
[0.07930076 0.07930076]	0.009471032135477047	83
[0.07747796 0.07747796]	0.009110879482523235	84
[0.07566899 0.07566899]	0.008757282022810418	85
[0.07387489 0.07387489]	0.008410533276236762	86
[0.07209667 0.07209667]	0.008070906254602977	87
[0.07033531 0.07033531]	0.007738652481558527	88
[0.06859176 0.06859176]	0.007414001156570364	89
[0.06686694 0.06686694]	0.007097158469209606	90
[0.06516172 0.06516172]	0.0067883070682847125	91
[0.06347696 0.06347696]	0.006487605688524489	92
[0.06181345 0.06181345]	0.006195188935681534	93
[0.06017198 0.06017198]	0.005911167229092196	94
[0.05855326 0.05855326]	0.005635626898953724	95
[0.05695796 0.05695796]	0.005368630433870282	96
[0.05538674 0.05538674]	0.005110216872624309	97
[0.05384017 0.05384017]	0.004860402332652406	98
[0.0523188 0.0523188]	0.004619180666398659	99
[0.05082312 0.05082312]	0.004386524235562022	100
[0.04935359 0.04935359]	0.004162384792297757	101
[0.0479106 0.0479106]	0.003946694455662684	102
[0.04649451 0.04649451]	0.003739366771024543	103
[0.04510562 0.04510562]	0.0035402978397843406	104
[0.0437442 0.0437442]	0.0033493675065847757	105
[0.04241045 0.04241045]	0.0031664405911896133	106
[0.04110454 0.04110454]	0.0029913681524116327	107
[0.0398266 0.0398266]	0.002823988771812003	108
[0.0385767 0.0385767]	0.0026641298453995883	109
[0.03735488 0.03735488]	0.0025116088721840162	110
[0.03616115 0.03616115]	0.0023662347291712976	111
[0.03499544 0.03499544]	0.002227808923221081	112
[0.03385768 0.03385768]	0.002096126811077554	113
[0.03274776 0.03274776]	0.001970978779829355	114
[0.03166552 0.03166552]	0.0018521513810318142	115
[0.03061077 0.03061077]	0.0017394284127048485	116
[0.0295833 0.0295833]	0.0016325919444068876	117
[0.02858286 0.02858286]	0.0015314232815397497	118
[0.02760917 0.02760917]	0.001435703865969758	119
[0.02666194 0.02666194]	0.0013452161109320454	120
[0.02574084 0.02574084]	0.0012597441690125495	121
[0.02484552 0.02484552]	0.001179074632770029	122
[0.02397562 0.02397562]	0.001102997168258484	123
[0.02313076 0.02313076]	0.0010313050823431134	124
[0.02231052 0.02231052]	0.0009637958252554067	125
[0.0215145 0.0215145]	0.0009002714303206027	126
[0.02074227 0.02074227]	0.0008405388932003743	127
[0.01999338 0.01999338]	0.0007844104933347607	128
[0.01926738 0.01926738]	0.0007317040605428159	129
[0.01856381 0.01856381]	0.0006822431899514119	130
[0.01788221 0.01788221]	0.0006358574085730946	131
[0.01722209 0.01722209]	0.0005923822969516482	132
[0.01658299 0.01658299]	0.0005516595693425212	133
[0.01596441 0.01596441]	0.0005135371158985923	134
[0.01536588 0.01536588]	0.00047786901029846864	135
[0.01478692 0.01478692]	0.0004445154861861646	136
[0.01422703 0.01422703]	0.0004133428856947098	137
[0.01368574 0.01368574]	0.0003842235832073654	138
[0.01316255 0.01316255]	0.0003570358873697328	139
[0.01265701 0.01265701]	0.00033166392421483536	140
[0.01216862 0.01216862]	0.0003079975040960318	141
[0.01169692 0.01169692]	0.00028593197495247396	142
[0.01124144 0.01124144]	0.00026536806425459664	143
[0.01080172 0.01080172]	0.0002462117117987103	144
[0.01037731 0.01037731]	0.00022837389534282435	145
[0.00996775 0.00996775]	0.00021177045090091796	146
[0.00957262 0.00957262]	0.0001963218893420302	147
[0.00919146 0.00919146]	0.00018195321077671775	148
[0.00882387 0.00882387]	0.000168593718055502	149
[0.00846941 0.00846941]	0.00015617683055352998	150
[0.00812768 0.00812768]	0.0001446398992749004	151
[0.00779828 0.00779828]	0.0001339240241768505	152
[0.00748082 0.00748082]	0.00012397387449037303	153
[0.0071749 0.0071749]	0.000114737512699174	154
[0.00688016 0.00688016]	0.00010616622273352944	155
[0.00659622 0.00659622]	9.821434283851575e-05	156
[0.00632274 0.00632274]	9.08391034888525e-05	157
[0.00605935 0.00605935]	8.400047064208593e-05	158
[0.00580573 0.00580573]	7.766099455120823e-05	159
[0.00556154 0.00556154]	7.17856642930692e-05	160
[0.00532645 0.00532645]	6.63417681125835e-05	161
[0.00510016 0.00510016]	6.129875963233148e-05	162
[0.00488236 0.00488236]	5.6628129933378544e-05	163
[0.00467276 0.00467276]	5.23032854751192e-05	164
[0.00447106 0.00447106]	4.829943178895962e-05	165
[0.00427699 0.00427699]	4.459346285271314e-05	166
[0.00409028 0.00409028]	4.116385602937666e-05	167
[0.00391066 0.00391066]	3.799057243413012e-05	168
[0.00373789 0.00373789]	3.505496257755243e-05	169
[0.00357171 0.00357171]	3.2339677120730474e-05	170
[0.0034119 0.0034119]	2.982858256774279e-05	171
[0.0032582 0.0032582]	2.7506681714183043e-05	172
[0.00311041 0.00311041]	2.5360038665186197e-05	173
[0.00296831 0.00296831]	2.337570823368496e-05	174
[0.00283169 0.00283169]	2.154166952822405e-05	175
[0.00270034 0.00270034]	1.9846763539975257e-05	176
[0.00257407 0.00257407]	1.8280634540178872e-05	177
[0.00245269 0.00245269]	1.6833675101623048e-05	178
[0.00233602 0.00233602]	1.549697456151136e-05	179
[0.00222389 0.00222389]	1.4262270747130963e-05	180
[0.00211612 0.00211612]	1.3121904790621107e-05	181
[0.00201254 0.00201254]	1.206877886445294e-05	182
[0.00191301 0.00191301]	1.1096316674962034e-05	183
[0.00181737 0.00181737]	1.0198426557197656e-05	184
[0.00172546 0.00172546]	9.36946702044605e-06	185
[0.00163716 0.00163716]	8.60421460020984e-06	186
[0.00155231 0.00155231]	7.897833878607748e-06	187
[0.0014708 0.0014708]	7.245849541505941e-06	188
[0.00139249 0.00139249]	6.644120347093789e-06	189
[0.00131725 0.00131725]	6.088814886589323e-06	190
[0.00124498 0.00124498]	5.576389024080719e-06	191
[0.00117555 0.00117555]	5.103564908254004e-06	192
[0.00110886 0.00110886]	4.667311454629785e-06	193
[0.0010448 0.0010448]	4.26482620251418e-06	194
[0.00098327 0.00098327]	3.89351845623686e-06	195
[0.00092417 0.00092417]	3.5509936254760143e-06	196
[0.00086741 0.00086741]	3.2350386844359184e-06	197
[0.00081289 0.00081289]	2.9436086744619057e-06	198
[0.00076053 0.00076053]	2.6748141791812922e-06	199
[0.00071025 0.00071025]	2.4269097056574906e-06	200
[0.00066196 0.00066196]	2.1982829091729086e-06	201
[0.00061559 0.00061559]	1.9874446031613262e-06	202
[0.00057106 0.00057106]	1.7930194995873036e-06	203
[0.00052829 0.00052829]	1.613737628526414e-06	204
[0.00048723 0.00048723]	1.4484263891181658e-06	205
[0.0004478 0.0004478]	1.2960031871400677e-06	206
[0.00040993 0.00040993]	1.1554686174483923e-06	207
[0.00037357 0.00037357]	1.025900152341892e-06	208
[0.00033867 0.00033867]	9.064462994919141e-07	209
[0.00030515 0.00030515]	7.963211955915816e-07	210
[0.00027296 0.00027296]	6.947996041620743e-07	211
[0.00024206 0.00024206]	6.01212288158414e-07	212
[0.00021239 0.00021239]	5.14941730029167e-07	213
[0.00018391 0.00018391]	4.3541817380762416e-07	214
[0.00015656 0.00015656]	3.621159655820409e-07	215
[0.0001303 0.0001303]	2.9455017038155757e-07	216
[0.0001051 0.0001051]	2.3227344505032461e-07	217
[8.08945057e-05 8.08945057e-05]	1.748731481504906e-07	218
[5.76602959e-05 5.76602959e-05]	1.2196866929042707e-07	219
[3.53546819e-05 3.53546819e-05]	7.320896153659465e-08	220

(array([3.53546819e-05, 3.53546819e-05]), 220)

FISTA算法（fista）

oh.fista.[函数名]([目标函数], [参数表], [初始迭代点], [正则化参数], [邻近算子名])

方法头	解释
normal(funcs: FuncArray, args: ArgArray, x_0: PointArray, mu: float=1e-3, proxim: str=“L1”, tk: float=0.02, verbose: bool=False, draw: bool=True, output_f: bool=False, epsilon: float=1e-6, k: int=0) -> OutputType	两步计算一个新点
variant(funcs: FuncArray, args: ArgArray, x_0: PointArray, mu: float=1e-3, proxim: str=“L1”, tk: float=0.02, verbose: bool=False, draw: bool=True, output_f: bool=False, epsilon: float=1e-6, k: int=0) -> OutputType	normal法的等价变形
decline(funcs: FuncArray, args: ArgArray, x_0: PointArray, mu: float=1e-3, proxim: str=“L1”, tk: float=0.02, verbose: bool=False, draw: bool=True, output_f: bool=False, epsilon: float=1e-6, k: int=0) -> OutputType	基于函数下降趋势的变体

oh.fista.normal(f, x, x_0, verbose=True, epsilon=1e-4)

(0.2, 0.2)	0.033830304000793295	0
[0.19925643 0.19925643]	0.03371630105707655	1
[0.19849759 0.19849759]	0.033599113758384015	2
[0.19752965 0.19752965]	0.03344840822740475	3
[0.19634058 0.19634058]	0.03326140386972337	4
[0.19491599 0.19491599]	0.03303467660717308	5
[0.19323907 0.19323907]	0.03276408584834668	6
[0.19129038 0.19129038]	0.03244469143441093	7
[0.18904782 0.18904782]	0.03207066253319544	8
[0.18648645 0.18648645]	0.03163518232735821	9
[0.18357846 0.18357846]	0.031130355220309	10
[0.18029315 0.18029315]	0.03054712756229315	11
[0.17659697 0.17659697]	0.02987523906813377	12
[0.17245376 0.17245376]	0.029103230710925534	13
[0.16782507 0.16782507]	0.028218546457533245	14
[0.16267078 0.16267078]	0.02720778105084813	15
[0.15695006 0.15695006]	0.02605714379032019	16
[0.15062263 0.15062263]	0.02475322722482501	17
[0.1436507 0.1436507]	0.023284185711105593	18
[0.13600142 0.13600142]	0.02164143378200551	19
[0.12765019 0.12765019]	0.019821954357666566	20
[0.11858478 0.11858478]	0.017831241286453643	21
[0.10881027 0.10881027]	0.01568676317570666	22
[0.09835481 0.09835481]	0.01342160091785943	23
[0.08727586 0.08727586]	0.01108757276749394	24
[0.0756663 0.0756663]	0.008756758818819103	25
[0.06365966 0.06365966]	0.006519996602965627	26
[0.05143318 0.05143318]	0.004480874877680786	27
[0.03920737 0.03920737]	0.0027443108743679394	28
[0.0272407 0.0272407]	0.0014001940854970719	29
[0.01581839 0.01581839]	0.0005047242448837863	30
[0.00523537 0.00523537]	6.4288746819883e-05	31
[-0.00418665 -0.00418665]	4.3944790650174575e-05	32
[-0.01221648 -0.01221648]	0.0003358041809499229	33
[-0.01868558 -0.01868558]	0.000782018176888592	34
[-0.02349934 -0.02349934]	0.001243963960329223	35
[-0.02664181 -0.02664181]	0.001608014900872538	36
[-0.02817331 -0.02817331]	0.0018038384618738578	37
[-0.02822152 -0.02822152]	0.001810201114210672	38
[-0.02696779 -0.02696779]	0.0016486746491471192	39
[-0.02463074 -0.02463074]	0.0013692472198611092	40
[-0.02144946 -0.02144946]	0.001033310326812164	41
[-0.01766789 -0.01766789]	0.0006987912458611627	42
[-0.01352189 -0.01352189]	0.0004102193974182509	43
[-0.00922928 -0.00922928]	0.0001943611548287423	44
[-0.00498303 -0.00498303]	6.0496796608013615e-05	45
[-0.00094732 -0.00094732]	3.6954413794614425e-06	46
[0.00270463 0.00270463]	1.9901129925390336e-05	47
[0.00587664 0.00587664]	7.94091094216332e-05	48
[0.00850264 0.00850264]	0.00015732135728718983	49
[0.01054374 0.01054374]	0.00023529252758100567	50
[0.01198517 0.01198517]	0.00029932348310261373	51
[0.0128333 0.0128333]	0.00034041104566886213	52
[0.01311286 0.01311286]	0.0003545027009827691	53
[0.01286437 0.01286437]	0.0003419638510109866	54
[0.01214176 0.01214176]	0.0003067200850132879	55
[0.01100998 0.01100998]	0.00025519907496466464	56
[0.0095427 0.0095427]	0.00019517498982886958	57
[0.00781981 0.00781981]	0.00013461228868992265	58
[0.00592486 0.00592486]	8.060873795925052e-05	59
[0.00394224 0.00394224]	3.853955135280601e-05	60
[0.00195435 0.00195435]	1.149547685501415e-05	61
[3.86693674e-05 3.86693674e-05]	8.032897007816521e-08	62
[-0.00169515 -0.00169515]	9.17148721695113e-06	63
[-0.00319296 -0.00319296]	2.7004334602874763e-05	64
[-0.00441392 -0.00441392]	4.8397238412822366e-05	65
[-0.00533136 -0.00533136]	6.857481635587594e-05	66
[-0.00593302 -0.00593302]	8.373629979419888e-05	67
[-0.0062205 -0.0062205]	9.15235913915823e-05	68
[-0.0062082 -0.0062082]	9.118306879630649e-05	69
[-0.00592161 -0.00592161]	8.34343820763833e-05	70
[-0.0053953 -0.0053953]	7.01133065277566e-05	71
[-0.00467068 -0.00467068]	5.368776346101515e-05	72
[-0.00379356 -0.00379356]	3.6752630190872105e-05	73
[-0.00281189 -0.00281189]	2.1593233635829933e-05	74
[-0.00177358 -0.00177358]	9.877481468752762e-06	75
[-0.00072459 -0.00072459]	2.501921465760068e-06	76
[0.00025271 0.00025271]	6.330306539194115e-07	77
[0.00112552 0.00112552]	4.7746896689738605e-06	78
[0.00186791 0.00186791]	1.0668443587263032e-05	79
[0.00246108 0.00246108]	1.6931895980111533e-05	80
[0.00289345 0.00289345]	2.2361878461997472e-05	81
[0.00316041 0.00316041]	2.6076758170315184e-05	82
[0.00326391 0.00326391]	2.7591230673255495e-05	83
[0.00321191 0.00321191]	2.682517662881479e-05	84
[0.00301765 0.00301765]	2.405576611892222e-05	85
[0.00269879 0.00269879]	1.9827263265911833e-05	86
[0.00227655 0.00227655]	1.4835994988390612e-05	87
[0.00177463 0.00177463]	9.808812559984457e-06	88
[0.00121826 0.00121826]	5.392209040060288e-06	89
[0.00063314 0.00063314]	2.0662326628037452e-06	90
[4.4412847e-05 4.4412847e-05]	9.277008269260652e-08	91
[-0.00048426 -0.00048426]	1.4383293148952407e-06	92
[-0.00093604 -0.00093604]	3.6301580781364767e-06	93
[-0.00129827 -0.00129827]	5.9828727580486845e-06	94
[-0.00156272 -0.00156272]	8.03638649505745e-06	95
[-0.00172564 -0.00172564]	9.442956816861173e-06	96
[-0.00178759 -0.00178759]	1.000614664689354e-05	97
[-0.00175314 -0.00175314]	9.691006528007353e-06	98
[-0.0016304 -0.0016304]	8.607546021477958e-06	99
[-0.00143044 -0.00143044]	6.973690459175214e-06	100
[-0.00116663 -0.00116663]	5.066443040807669e-06	101
[-0.00085394 -0.00085394]	3.170660486780329e-06	102
[-0.0005082 -0.0005082]	1.5338563099619648e-06	103
[-0.00014544 -0.00014544]	3.33212610205221e-07	104
[0.00017878 0.00017878]	4.214390667731358e-07	105
[0.00045421 0.00045421]	1.3203776625245732e-06	106
[0.00067324 0.00067324]	2.250832733219641e-06	107
[0.00083097 0.00083097]	3.038967555581645e-06	108
[0.00092526 0.00092526]	3.557218652962131e-06	109
[0.00095658 0.00095658]	3.737100302233256e-06	110
[0.0009278 0.0009278]	3.5716314819327603e-06	111
[0.00084399 0.00084399]	3.1084058923828957e-06	112
[0.00071203 0.00071203]	2.4354998352661786e-06	113
[0.00054025 0.00054025]	1.6631435338735005e-06	114
[0.00033803 0.00033803]	9.043319121947985e-07	115
[0.00011537 0.00011537]	2.573406355634432e-07	116
[-7.75729405e-05 -7.75729405e-05]	1.671842709922099e-07	117
[-0.00023501 -0.00023501]	5.805689223087464e-07	118
[-0.00035294 -0.00035294]	9.55330129339356e-07	119
[-0.00042919 -0.00042919]	1.2273575895614658e-06	120
[-0.00046338 -0.00046338]	1.3569078800428007e-06	121
[-0.00045682 -0.00045682]	1.3316868956475513e-06	122
[-0.00041237 -0.00041237]	1.1653229296710031e-06	123
[-0.0003342 -0.0003342]	8.920309869145119e-07	124
[-0.00022756 -0.00022756]	5.587686146122985e-07	125
[-9.85008103e-05 -9.85008103e-05]	2.1641313021020493e-07	126
[6.43207414e-06 6.43207414e-06]	1.2946889566740209e-08	127

(array([6.43207414e-06, 6.43207414e-06]), 127)

Nesterov算法（nesterov）

oh.nesterov.[函数名]([目标函数], [参数表], [初始迭代点], [正则化参数], [邻近算子名])

方法头	解释
seckin(funcs: FuncArray, args: ArgArray, x_0: PointArray, mu: float=1e-3, proxim: str=“L1”, tk: float=0.02, verbose: bool=False, draw: bool=True, output_f: bool=False, epsilon: float=1e-6, k: int=0) -> OutputType	第二类Nesterov加速法
accer(funcs: FuncArray, args: ArgArray, x_0: PointArray, mu: float=1e-3, proxim: str=“L1”, lk: float=0.01, tk: float=0.02, verbose: bool=False, draw: bool=True, output_f: bool=False, epsilon: float=1e-6, k: int=0) -> OutputType	复合优化算法的加速框架

(0.2, 0.2)	0.033830304000793295	0
[0.19925643 0.19925643]	0.03371630105707655	1
[0.19873208 0.19873208]	0.033635416161269645	2
[0.19824625 0.19824625]	0.033560113282182814	3
[0.19779193 0.19779193]	0.03348937977771688	4
[0.1973583 0.1973583]	0.03342158708171633	5
[0.19693596 0.19693596]	0.03335529505960039	6
[0.19651836 0.19651836]	0.03328949344326663	7
[0.19610149 0.19610149]	0.03322355499940229	8
[0.19568304 0.19568304]	0.033157115543780515	9
[0.19526174 0.19526174]	0.033089970332591104	10
[0.19483691 0.19483691]	0.033022004801464444	11
[0.19440817 0.19440817]	0.032953153342586375	12
[0.19397531 0.19397531]	0.03288337625764423	13
[0.19353821 0.19353821]	0.032812647334081416	14
[0.1930968 0.1930968]	0.03274094729563452	15
[0.19265102 0.19265102]	0.03266826039819621	16
[0.19220083 0.19220083]	0.032594572677139846	17
[0.19174619 0.19174619]	0.032519871051184146	18
[0.19128706 0.19128706]	0.03244414286707404	19
[0.19082343 0.19082343]	0.032367375670024706	20
[0.19035525 0.19035525]	0.0322895570894612	21
[0.1898825 0.1898825]	0.03221067478356757	22
[0.18940514 0.18940514]	0.03213071641385224	23
[0.18892316 0.18892316]	0.03204966963507849	24
[0.18843651 0.18843651]	0.031967522093123764	25
[0.18794517 0.18794517]	0.03188426142698723	26
[0.18744912 0.18744912]	0.03179987527304022	27
[0.18694832 0.18694832]	0.031714351270546136	28
[0.18644275 0.18644275]	0.03162767706796477	29
[0.18593238 0.18593238]	0.03153984032980098	30
[0.18541719 0.18541719]	0.03145082874386781	31
[0.18489715 0.18489715]	0.03136063002891287	32
[0.18437222 0.18437222]	0.03126923194257793	33
[0.1838424 0.1838424]	0.031176622289681582	34
[0.18330765 0.18330765]	0.03108278893081914	35
[0.18276794 0.18276794]	0.03098771979128425	36
[0.18222326 0.18222326]	0.03089140287031154	37
[0.18167359 0.18167359]	0.030793826250645626	38
[0.18111889 0.18111889]	0.030694978108438714	39
[0.18055915 0.18055915]	0.03059484672348252	40
[0.17999435 0.17999435]	0.030493420489773625	41
[0.17942446 0.17942446]	0.030390687926420742	42
[0.17884946 0.17884946]	0.03028663768889194	43
[0.17826935 0.17826935]	0.030181258580608418	44
[0.17768409 0.17768409]	0.030074539564881035	45
[0.17709367 0.17709367]	0.02996646977719818	46
[0.17649807 0.17649807]	0.029857038537858628	47
[0.17589728 0.17589728]	0.02974623536495526	48
[0.17529127 0.17529127]	0.02963404998770624	49
[0.17468005 0.17468005]	0.029520472360134945	50
[0.17406359 0.17406359]	0.029405492675093462	51
[0.17344188 0.17344188]	0.029289101378632255	52
[0.1728149 0.1728149]	0.029171289184710302	53
[0.17218266 0.17218266]	0.029052047090239855	54
[0.17154513 0.17154513]	0.028931366390468057	55
[0.17090231 0.17090231]	0.028809238694680148	56
[0.17025419 0.17025419]	0.028685655942228945	57
[0.16960076 0.16960076]	0.028560610418873568	58
[0.16894202 0.16894202]	0.028434094773425688	59
[0.16827797 0.16827797]	0.028306102034691773	60
[0.1676086 0.1676086]	0.02817662562869971	61
[0.16693391 0.16693391]	0.028045659396202398	62
[0.1662539 0.1662539]	0.027913197610440834	63
[0.16556856 0.16556856]	0.0277792349951582	64
[0.16487791 0.16487791]	0.027643766742844578	65
[0.16418194 0.16418194]	0.027506788533203375	66
[0.16348066 0.16348066]	0.02736829655181286	67
[0.16277408 0.16277408]	0.02722828750897477	68
[0.1620622 0.1620622]	0.027086758658721198	69
[0.16134503 0.16134503]	0.02694370781796281	70
[0.16062258 0.16062258]	0.026799133385756447	71
[0.15989486 0.15989486]	0.026653034362663773	72
[0.1591619 0.1591619]	0.026505410370182444	73
[0.15842369 0.15842369]	0.026356261670214508	74
[0.15768027 0.15768027]	0.026205589184552146	75
[0.15693165 0.15693165]	0.026053394514344092	76
[0.15617784 0.15617784]	0.02589967995951506	77
[0.15541887 0.15541887]	0.025744448538108148	78
[0.15465477 0.15465477]	0.02558770400550724	79
[0.15388556 0.15388556]	0.025429450873514402	80
[0.15311126 0.15311126]	0.0252696944292389	81
[0.15233191 0.15233191]	0.02510844075376142	82
[0.15154753 0.15154753]	0.0249456967405326	83
[0.15075817 0.15075817]	0.024781470113468172	84
[0.14996385 0.14996385]	0.024615769444693614	85
[0.14916461 0.14916461]	0.02444860417189907	86
[0.14836049 0.14836049]	0.024279984615258984	87
[0.14755153 0.14755153]	0.02410992199386683	88
[0.14673778 0.14673778]	0.023938428441643678	89
[0.14591927 0.14591927]	0.02376551702266892	90
[0.14509606 0.14509606]	0.023591201745887268	91
[0.14426819 0.14426819]	0.02341549757913816	92
[0.14343572 0.14343572]	0.023238420462463397	93
[0.1425987 0.1425987]	0.02305998732063617	94
[0.14175718 0.14175718]	0.022880216074865917	95
[0.14091122 0.14091122]	0.022699125653621477	96
[0.14006088 0.14006088]	0.022516736002528296	97
[0.13920622 0.13920622]	0.022333068093279024	98
[0.13834731 0.13834731]	0.022148143931513993	99
[0.13748421 0.13748421]	0.02196198656361456	100
[0.136617 0.136617]	0.021774620082362042	101
[0.13574573 0.13574573]	0.02158606963140784	102
[0.13487049 0.13487049]	0.02139636140851093	103
[0.13399135 0.13399135]	0.02120552266748679	104
[0.13310839 0.13310839]	0.021013581718826876	105
[0.13222168 0.13222168]	0.020820567928938712	106
[0.13133131 0.13133131]	0.020626511717963182	107
[0.13043736 0.13043736]	0.02043144455612627	108
[0.12953992 0.12953992]	0.020235398958584165	109
[0.12863908 0.12863908]	0.02003840847872382	110
[0.12773492 0.12773492]	0.01984050769987993	111
[0.12682754 0.12682754]	0.019641732225440522	112
[0.12591704 0.12591704]	0.019442118667302975	113
[0.1250035 0.1250035]	0.019241704632659312	114
[0.12408704 0.12408704]	0.019040528709081284	115
[0.12316775 0.12316775]	0.018838630447888367	116
[0.12224573 0.12224573]	0.018636050345776825	117
[0.12132109 0.12132109]	0.018432829824700743	118
[0.12039394 0.12039394]	0.01822901120999248	119
[0.11946438 0.11946438]	0.01802463770671741	120
[0.11853253 0.11853253]	0.017819753374264793	121
[0.1175985 0.1175985]	0.017614403099174197	122
[0.11666241 0.11666241]	0.017408632566209822	123
[0.11572436 0.11572436]	0.01720248822769215	124
[0.11478448 0.11478448]	0.016996017271108478	125
[0.11384289 0.11384289]	0.016789267585023703	126
[0.11289972 0.11289972]	0.016582287723316894	127
[0.11195507 0.11195507]	0.01637512686778442	128
[0.11100909 0.11100909]	0.016167834789139506	129
[0.11006189 0.11006189]	0.015960461806458145	130
[0.1091136 0.1091136]	0.015753058745119824	131
[0.10816436 0.10816436]	0.015545676893292247	132
[0.10721428 0.10721428]	0.015338367957028396	133
[0.10626351 0.10626351]	0.015131184014033131	134
[0.10531218 0.10531218]	0.014924177466172134	135
[0.10436042 0.10436042]	0.014717400990799457	136
[0.10340836 0.10340836]	0.014510907490978745	137
[0.10245615 0.10245615]	0.014304750044688593	138
[0.10150391 0.10150391]	0.014098981853094075	139
[0.10055179 0.10055179]	0.013893656187982946	140
[0.09959992 0.09959992]	0.01368882633845935	141
[0.09864844 0.09864844]	0.013484545556998294	142
[0.09769749 0.09769749]	0.013280867004964954	143
[0.09674722 0.09674722]	0.013077843697704697	144
[0.09579776 0.09579776]	0.01287552844931507	145
[0.09484925 0.09484925]	0.01267397381721372	146
[0.09390183 0.09390183]	0.012473232046613741	147
[0.09295564 0.09295564]	0.012273355015029202	148
[0.09201083 0.09201083]	0.012074394176923015	149
[0.09106754 0.09106754]	0.011876400508619371	150
[0.09012589 0.09012589]	0.011679424453601839	151
[0.08918605 0.08918605]	0.011483515868314823	152
[0.08824814 0.08824814]	0.01128872396858924	153
[0.0873123 0.0873123]	0.011095097276812349	154
[0.08637867 0.08637867]	0.010902683569959014	155
[0.0854474 0.0854474]	0.010711529828601291	156
[0.08451862 0.08451862]	0.01052168218701202	157
[0.08359246 0.08359246]	0.010333185884471796	158
[0.08266906 0.08266906]	0.01014608521789343	159
[0.08174856 0.08174856]	0.00996042349586558	160
[0.08083108 0.08083108]	0.009776242994221208	161
[0.07991677 0.07991677]	0.009593584913228696	162
[0.07900575 0.07900575]	0.009412489336499564	163
[0.07809816 0.07809816]	0.009232995191701765	164
[0.07719411 0.07719411]	0.009055140213166078	165
[0.07629375 0.07629375]	0.008878960906460193	166
[0.07539718 0.07539718]	0.008704492515007505	167
[0.07450455 0.07450455]	0.008531768988817391	168
[0.07361596 0.07361596]	0.008360822955386055	169
[0.07273153 0.07273153]	0.008191685692826979	170
[0.0718514 0.0718514]	0.008024387105275749	171
[0.07097566 0.07097566]	0.007858955700613185	172
[0.07010445 0.07010445]	0.007695418570540102	173
[0.06923786 0.06923786]	0.007533801373033395	174
[0.068376 0.068376]	0.007374128317203251	175
[0.06751899 0.06751899]	0.007216422150565665	176
[0.06666693 0.06666693]	0.007060704148737249	177
[0.06581992 0.06581992]	0.006906994107553427	178
[0.06497806 0.06497806]	0.00675531033760118	179
[0.06414146 0.06414146]	0.006605669661154516	180
[0.06331019 0.06331019]	0.006458087411491039	181
[0.06248436 0.06248436]	0.006312577434564489	182
[0.06166406 0.06166406]	0.006169152092997068	183
[0.06084938 0.06084938]	0.006027822272356063	184
[0.06004039 0.06004039]	0.005888597389665743	185
[0.05923718 0.05923718]	0.005751485404107095	186
[0.05843983 0.05843983]	0.005616492829845886	187
[0.05764842 0.05764842]	0.005483624750930617	188
[0.05686301 0.05686301]	0.0053528848381917	189
[0.05608369 0.05608369]	0.00522427536807383	190
[0.05531051 0.05531051]	0.005097797243323587	191
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