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import optimtool as oo
from optimtool.base import np, sp, plt
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pip install optimtool>=2.5.0
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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]) ϕ ( x ) = f ( x ) + h ( x ) \phi(x) = f(x) + h(x) ϕ(x)=f(x)+h(x)
其中 f ( x ) f(x) f(x)是可微的。 h ( x ) h(x) 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 ) h(x) h(x)有： ∣ ∣ x ∣ ∣ 1 ||x||1 ∣∣x∣∣1, ∣ ∣ x ∣ ∣ 2 ||x||2 ∣∣x∣∣2, − ∑ i ln ( x i ) -\sum {i}{\ln(x_i)} −∑iln(xi)，实例： {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] f(x)=i=1∑n((n−j=1∑ncosxj)+i(1−cosxi)−sinxi)2,x0=[0.2,0.2,...,0.2]
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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）
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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
python
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oh.approt.grad(f, x, x_0, verbose=True, epsilon=1e-4)
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(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
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(array([3.53546819e-05, 3.53546819e-05]), 220) FISTA算法（fista）
python
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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
python
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oh.fista.normal(f, x, x_0, verbose=True, epsilon=1e-4)
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(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
text
复制代码
(array([6.43207414e-06, 6.43207414e-06]), 127) Nesterov算法（nesterov）
python
复制代码
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
text
复制代码
(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
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[0.19035525 0.19035525] 0.0322895570894612 21
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[0.18843651 0.18843651] 0.031967522093123764 25
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[0.17826935 0.17826935] 0.030181258580608418 44
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[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
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[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
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[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
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[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
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[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
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[0.08174856 0.08174856] 0.00996042349586558 160
[0.08083108 0.08083108] 0.009776242994221208 161
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[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
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[0.06923786 0.06923786] 0.007533801373033395 174
[0.068376 0.068376] 0.007374128317203251 175
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[0.06497806 0.06497806] 0.00675531033760118 179
[0.06414146 0.06414146] 0.006605669661154516 180
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[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
[0.05454354 0.05454354] 0.00497345001545756 192
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[0.05302849 0.05302849] 0.004731139846886088 194
[0.05228051 0.05228051] 0.004613169478506701 195
[0.05153898 0.05153898] 0.004497315207696919 196
[0.05080394 0.05080394] 0.004383570223184056 197
[0.05007544 0.05007544] 0.004271926529837656 198
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[0.04863823 0.04863823] 0.004054905312763828 200
[0.0479296 0.0479296] 0.003949506176988748 201
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[0.03811758 0.03811758] 0.002606378996397809 216
[0.03751857 0.03751857] 0.0025318245935165348 217
[0.03692646 0.03692646] 0.0024590182419483536 218
[0.03634126 0.03634126] 0.0023879355346878837 219
[0.03576293 0.03576293] 0.002318551698819148 220
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[0.03406913 0.03406913] 0.0021203409415594945 223
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text
复制代码
(array([2.93106273e-05, 2.93106273e-05]), 444) 
