我已经建立了一个具有线性等式约束的优化问题如下

sol0 = minimize(objective, x0, args=mock_df, method='trust-constr',
                bounds=bnds, constraints=cons,
                options={'maxiter': 250, 'verbose': 3})

objective是加权和函数，其系数/权重将被优化以使其最小化。由于我在系数和约束上有边界，所以我使用了 trust-constr scipy.optimize.minimize 内的方法.

最小化可行，但我不明白终止条件。根据 trust-constr documentation它应该终止于 xtol

The algorithm will terminate when tr_radius < xtol, where tr_radius is the radius of the trust region used in the algorithm. Default is 1e-8.

然而，verbose输出显示，终止确实是由 barrier_tol 触发的参数，如您在下面的 list 中所见

| niter |f evals|CG iter|  obj func   |tr radius |   opt    |  c viol  | penalty  |barrier param|CG stop|
|-------|-------|-------|-------------|----------|----------|----------|----------|-------------|-------|
C:\ProgramData\Anaconda3\lib\site-packages\scipy\optimize\_trustregion_constr\projections.py:182: UserWarning: Singular Jacobian matrix. Using SVD decomposition to perform the factorizations.
  warn('Singular Jacobian matrix. Using SVD decomposition to ' +
|   1   |  31   |   0   | -4.4450e+02 | 1.00e+00 | 7.61e+02 | 5.00e-01 | 1.00e+00 |  1.00e-01   |   0   |
C:\ProgramData\Anaconda3\lib\site-packages\scipy\optimize\_hessian_update_strategy.py:187: UserWarning: delta_grad == 0.0. Check if the approximated function is linear. If the function is linear better results can be obtained by defining the Hessian as zero instead of using quasi-Newton approximations.
  'approximations.', UserWarning)
|   2   |  62   |   1   | -2.2830e+03 | 6.99e+00 | 3.64e+02 | 7.28e-01 | 1.00e+00 |  1.00e-01   |   2   |
|   3   |  93   |   2   | -9.7651e+03 | 3.42e+01 | 5.52e+01 | 5.33e+00 | 1.00e+00 |  1.00e-01   |   2   |
|   4   |  124  |  26   | -4.9999e+03 | 3.42e+01 | 8.23e+01 | 9.29e-01 | 3.48e+16 |  1.00e-01   |   1   |
|   5   |  155  |  50   | -4.1486e+03 | 3.42e+01 | 5.04e+01 | 2.08e-01 | 3.48e+16 |  1.00e-01   |   1   |
...
|  56   | 1674  | 1127  | -1.6146e+03 | 1.77e-08 | 4.49e+00 | 3.55e-15 | 3.66e+33 |  1.00e-01   |   1   |
|  57   | 1705  | 1151  | -1.6146e+03 | 1.77e-09 | 4.49e+00 | 3.55e-15 | 3.66e+33 |  1.00e-01   |   1   |
|  58   | 1736  | 1151  | -1.6146e+03 | 1.00e+00 | 4.42e+00 | 3.55e-15 | 1.00e+00 |  2.00e-02   |   0   |
|  59   | 1767  | 1175  | -1.6146e+03 | 1.00e-01 | 4.42e+00 | 3.55e-15 | 1.00e+00 |  2.00e-02   |   1   |
|  60   | 1798  | 1199  | -1.6146e+03 | 1.00e-02 | 4.42e+00 | 3.55e-15 | 1.00e+00 |  2.00e-02   |   1   |
...
|  66   | 1984  | 1343  | -1.6146e+03 | 1.00e-08 | 4.42e+00 | 3.55e-15 | 1.00e+00 |  2.00e-02   |   1   |
|  67   | 2015  | 1367  | -1.6146e+03 | 1.00e-09 | 4.42e+00 | 3.55e-15 | 1.00e+00 |  2.00e-02   |   1   |
|  68   | 2046  | 1367  | -1.6146e+03 | 1.00e+00 | 4.36e+00 | 3.55e-15 | 1.00e+00 |  4.00e-03   |   0   |
|  69   | 2077  | 1391  | -1.6146e+03 | 1.00e-01 | 4.36e+00 | 3.55e-15 | 1.00e+00 |  4.00e-03   |   1   |
...
|  77   | 2325  | 1583  | -1.6146e+03 | 1.00e-09 | 4.36e+00 | 3.55e-15 | 1.00e+00 |  4.00e-03   |   1   |
|  78   | 2356  | 1583  | -1.6146e+03 | 1.00e+00 | 4.35e+00 | 3.55e-15 | 1.00e+00 |  8.00e-04   |   0   |
|  79   | 2387  | 1607  | -1.6146e+03 | 1.00e-01 | 4.35e+00 | 3.55e-15 | 1.00e+00 |  8.00e-04   |   1   |
...
|  87   | 2635  | 1799  | -1.6146e+03 | 1.00e-09 | 4.35e+00 | 3.55e-15 | 1.00e+00 |  8.00e-04   |   1   |
|  88   | 2666  | 1799  | -1.6146e+03 | 1.00e+00 | 4.34e+00 | 3.55e-15 | 1.00e+00 |  1.60e-04   |   0   |
|  89   | 2697  | 1823  | -1.6146e+03 | 1.00e-01 | 4.34e+00 | 3.55e-15 | 1.00e+00 |  1.60e-04   |   1   |
...
|  97   | 2945  | 2015  | -1.6146e+03 | 1.00e-09 | 4.34e+00 | 3.55e-15 | 1.00e+00 |  1.60e-04   |   1   |
|  98   | 2976  | 2015  | -1.6146e+03 | 1.00e+00 | 4.34e+00 | 3.55e-15 | 1.00e+00 |  3.20e-05   |   0   |
|  99   | 3007  | 2039  | -1.6146e+03 | 1.00e-01 | 4.34e+00 | 3.55e-15 | 1.00e+00 |  3.20e-05   |   1   |
...
|  167  | 5053  | 3527  | -1.6146e+03 | 1.00e-07 | 1.35e+01 | 2.12e-11 | 1.00e+00 |  2.05e-09   |   1   |
|  168  | 5084  | 3551  | -1.6146e+03 | 1.00e-08 | 1.35e+01 | 2.12e-11 | 1.00e+00 |  2.05e-09   |   1   |
|  169  | 5115  | 3575  | -1.6146e+03 | 1.00e-09 | 1.35e+01 | 2.12e-11 | 1.00e+00 |  2.05e-09   |   1   |
`xtol` termination condition is satisfied.
Number of iterations: 169, function evaluations: 5115, CG iterations: 3575, optimality: 1.35e+01, constraint violation: 2.12e-11, execution time: 3.8e+02 s.

很明显，一次，tr_radius < xtol , tr_radius重置为其默认值 1和 barrier param降低了。一次barrier param < barrier_tol (即 1e-8)和 tr_radius < xtol , 优化成功终止。文档说关于 barrier_tol

When inequality constraints are present the algorithm will terminate only when the barrier parameter is less than barrier_tol.

这将解释不等式约束情况下的行为，但我所有的约束都是定义为字典的等式约束

con0 = {'type': 'eq', 'fun': constraint0}

有没有人足够深入trust-constr给我解释一下？

最佳答案

你有上限的变量吗？也许求解器将这些实现为约束，如 var < UPPER_BOUND .

(如果我有信誉评分，我会把它作为评论)

关于python - scipy.optimize.minimize(method='trust-constr') 不会在 xtol 条件下终止，我们在Stack Overflow上找到一个类似的问题： https://stackoverflow.com/questions/57107308/