继续我的标题，我在特定问题中比较了两种方法。对于容易的最小化问题，这不会发生，因此我将不得不在底部发布我的相当大的问题。定义
def objective(someArr):
o = coeff.dot(someArr)-expected
return o.dot(o)
我认为一个约束和一些界限是相同的并且意味着一切都必须是否定的：
constr = {'type':'ineq','fun': lambda x: x.min()}
bounds = [(0,None) for _ in range(len(expected))]
现在以两种不同的方式最小化（猜测是任意的）：
guess = [1 for _ in range(len(expected))]
minimize(objective,guess,constraints=constr,method='slsqp')
minimize(objective,guess,bounds=bounds,method='slsqp')
两者都成功了，但给出了不同的结果！它们是相似的，但受约束的版本似乎找到了一个“更好的解决方案”，因为它是连续的，我知道它不太可能（一些初始猜测保留原样）。看起来边界版本提供了更可靠的解决方案（包括中间的不连续性），任何想法为什么？ 为什么结果不同？
对于足够简单的系统来说，这不会发生，所以我的下面是：
预期
array([ 4.03735117e-02, 1.08637788e-02, 1.54964051e-02,
3.78628505e-02, 2.37030325e-02, 6.86859818e-01,
1.46476530e-01, 1.04440486e-03, 1.20711274e-01,
1.60280666e-01, 2.33949054e-02, 8.46002796e-03,
7.45780483e-04, 3.69392042e-02, 1.44665642e-03,
1.44608308e-02, 1.27347734e-02, 4.23352961e-04,
9.20542456e-02, 2.48495819e-03, 3.54655192e-01])
系数矩阵（21x21）：
[[ 9.37707100e-20 6.68400440e-18 6.97912430e-16 8.98556840e-14
1.07937057e-11 4.19849820e-10 2.73605280e-08 1.09170960e-06
1.50449010e-05 7.96266900e-05 2.31555200e-04 4.57569000e-04
5.90697100e-04 4.10655400e-04 1.63821000e-04 5.53010200e-05
1.09951060e-05 3.84831400e-06 1.23909470e-06 2.31528300e-07
5.02411300e-08]
[ 3.45748390e-15 1.16643780e-13 5.32307960e-12 1.01004120e-10
4.05216220e-09 1.61456490e-07 4.23295710e-06 6.24295200e-05
3.29901600e-04 6.66420600e-04 7.29823900e-04 5.27159300e-04
2.27278100e-04 4.42585700e-05 4.29081900e-06 4.30265500e-07
2.13397700e-08 4.01132800e-09 1.18220120e-09 1.31554450e-10
6.78713900e-12]
[ 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 1.85846486e-13
3.36231717e-10 1.85400562e-08 3.89468660e-07 5.55975320e-06
4.73904880e-05 1.54447990e-04 1.50380210e-04 5.69735990e-05
6.27187000e-06 9.82224200e-07 1.26135220e-07 1.16118950e-08
1.28288250e-09]
[ 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
2.43215800e-14 5.96589295e-12 3.51565120e-09 1.40006520e-07
3.61819670e-06 4.06318460e-05 1.32977260e-04 1.59613560e-04
6.96288200e-05 3.19618580e-05 1.17693300e-05 2.59929440e-06
6.08805400e-07]
[ 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
1.55452990e-11 6.12778810e-09 2.40761500e-07 3.84277600e-06
2.97983700e-05 1.56114000e-04 5.30523000e-04 1.07510900e-03
1.29982300e-03 8.48435000e-04 2.49909800e-04 4.34448700e-05
2.72827100e-06 3.61865000e-07 5.30180000e-08 5.39343000e-09
3.39819900e-10]
[ 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
9.80980000e-16 4.53215210e-13 5.93537000e-11 7.73680600e-09
1.45490800e-07 2.06500700e-06 1.85582600e-05 1.01621100e-04
3.65050000e-04 8.47504000e-04 9.16790000e-04 5.10335000e-04
1.32094200e-04 5.01662000e-05 1.68653100e-05 3.42706000e-06
7.64106000e-07]
[ 5.22393900e-16 9.57670700e-14 2.80224630e-11 6.17311800e-09
3.63986700e-07 1.27199100e-05 1.61234500e-04 6.80855000e-04
1.13993600e-03 1.09554200e-03 6.55816000e-04 2.29829600e-04
4.92989000e-05 5.25123200e-06 1.41564430e-07 2.39038170e-09
6.00416600e-12 6.19360000e-14 0.00000000e+00 0.00000000e+00
0.00000000e+00]
[ 0.00000000e+00 4.75768800e-19 1.25757632e-16 3.85615412e-14
1.64951977e-10 8.16844600e-09 1.44055600e-07 1.93038560e-06
1.65309040e-05 7.25888800e-05 1.53391160e-04 1.85548480e-04
1.41324560e-04 5.35520440e-05 9.08814400e-06 1.16508600e-06
6.51461200e-08 9.63840800e-09 1.89874880e-09 2.80790120e-10
1.77267480e-11]
[ 0.00000000e+00 0.00000000e+00 0.00000000e+00 3.12433680e-18
2.09937884e-15 6.15295200e-13 2.33827048e-10 9.42587360e-09
2.18070840e-07 2.53094400e-06 1.39357400e-05 4.56638000e-05
1.03468560e-04 1.37336160e-04 8.75893200e-05 3.60747400e-05
7.94232400e-06 2.86150800e-06 9.40383600e-07 1.83250080e-07
4.02287600e-08]
[ 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 2.78360280e-14
1.13077826e-10 1.65225720e-08 4.49710800e-07 4.18136400e-06
4.26663600e-06 1.14932400e-06 1.25458080e-07 2.73596400e-09
9.87835200e-11]
[ 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 4.18941677e-09 6.46043040e-06 4.35858800e-05
1.85997600e-05 3.43239200e-06 1.11978076e-07 5.19446488e-11
0.00000000e+00]
[ 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 1.57210000e-12 3.60625836e-09
3.30526520e-07 5.77426800e-06 1.33358320e-05 1.43552480e-06
3.02920760e-08]
[ 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
2.92584400e-12 2.03562744e-08 3.00648720e-06 3.84799520e-06
1.40841200e-07 4.38522680e-09 4.19531080e-11 0.00000000e+00
0.00000000e+00]
[ 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 8.04725600e-12 1.39600679e-07 7.36690800e-06
2.59910000e-05 2.70401200e-05 4.35387960e-06 9.09141480e-09
4.18099600e-12]
[ 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 7.54614320e-12
4.96265360e-09 1.12553828e-06 1.37813920e-05 2.78272760e-06
2.80655084e-09 3.01261760e-12 0.00000000e+00 0.00000000e+00
0.00000000e+00]
[ 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
7.84628000e-13 2.15015975e-08 1.03311776e-05 2.95554800e-05
4.24798800e-06 3.50478760e-07 5.99805920e-09 2.26524600e-12
0.00000000e+00]
[ 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 3.38659412e-10 1.68748108e-06 2.91162400e-05
3.32621600e-05 1.37055520e-05 9.31179320e-07 7.59133436e-10
1.19764000e-13]
[ 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
1.70595760e-13 8.46074200e-11 1.00050024e-08 5.02041840e-07
9.72964000e-06 4.00182400e-05 2.37195920e-05 4.51005344e-07
1.29503120e-11 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00]
[ 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 8.50672000e-14 5.96485392e-09 9.45778520e-07
1.02437720e-05 2.73561200e-05 1.05041560e-05 6.73162160e-08
9.48935360e-11]
[ 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
1.55824024e-11 4.39452984e-08 3.48200400e-06 2.59034680e-06
3.11364280e-08 3.22964640e-10 1.01458120e-12 0.00000000e+00
0.00000000e+00]
[ 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00
0.00000000e+00 0.00000000e+00 3.09492760e-13 3.68745010e-10
3.25169980e-08 1.59072640e-06 1.88484840e-05 5.89398200e-05
5.35469200e-05 3.43275000e-05 1.51554420e-05 3.76945800e-06
9.39956600e-07]]
答案 0 :(得分：1)
不同的计算产生不同的结果并不奇怪。您的约束在数学上等效于下限，但在SLSQP算法中，它们的处理方式不同。有一个非常简单的subroutine用于强制上/下限，而约束的处理深埋在那些2150行的Fortran中。
对于容易的最小化问题，这不太重要，因为算法很可能找到最佳解决方案。但是，由于难以最小化问题，您无法保证完美的结果。该算法将运行一段时间，试图改善结果，并最终决定停在看起来可能是最小的某个地方。它将停止的位置取决于您提供的所有参数。
最好将数字上/下限明确地作为边界给出（而不是作为不等式约束的特例），因为如果最小化例程接受与约束分开的边界，它可能有更有效的方法来处理它们。