Scipy.optimize：我应该如何正确编写约束？

Question

我想使用 scipy.optimize.minimize 求解 (2+x_1)/(1+x_2)-3x_1+4x_3 的最小值，x_1、x_2 和 x_3 的约束在 0.1 到 0.9 的范围内。 我的代码如下：

rest = [[0.1, 0.9], [0.1, 0.9], [0.1, 0.9]]
cons = [{'type': 'ineq', 'fun': lambda x: x[i]-0.1 if j == 0 else lambda x: 0.9-x[i]} for i in range(3) for j in range(2)]
# cons = [{'type': 'ineq', 'fun': lambda x: x[0]-0.1},
#        {'type': 'ineq', 'fun': lambda x: 0.9-x[0]},
#        {'type': 'ineq', 'fun': lambda x: x[1]-0.1},
#        {'type': 'ineq', 'fun': lambda x: 0.9-x[1]},
#        {'type': 'ineq', 'fun': lambda x: x[2]-0.1},
#        {'type': 'ineq', 'fun': lambda x: 0.9-x[2]}]
res2 = minimize(lambda x: (2 + x[0]) / (1 + x[1]) - 3 * x[0] + 4 * x[2], np.array((0.5, 0.5, 0.5)), method='SLSQP', constraints=cons)
res2.fun, res2.success, res2.x

运行它并报告 TypeError：

---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-7-3caab45922c2> in <module>
      7 #        {'type': 'ineq', 'fun': lambda x: x[2]-0.1},
      8 #        {'type': 'ineq', 'fun': lambda x: 0.9-x[2]}]
----> 9 res2 = minimize(lambda x: (2 + x[0]) / (1 + x[1]) - 3 * x[0] + 4 * x[2], np.array((0.5, 0.5, 0.5)), method='SLSQP', constraints=cons)
     10 res2.fun, res2.success, res2.x

~\anaconda3\lib\site-packages\scipy\optimize\_minimize.py in minimize(fun, x0, args, method, jac, hess, hessp, bounds, constraints, tol, callback, options)
    623         return _minimize_cobyla(fun, x0, args, constraints, **options)
    624     elif meth == 'slsqp':
--> 625         return _minimize_slsqp(fun, x0, args, jac, bounds,
    626                                constraints, callback=callback, **options)
    627     elif meth == 'trust-constr':

~\anaconda3\lib\site-packages\scipy\optimize\slsqp.py in _minimize_slsqp(func, x0, args, jac, bounds, constraints, maxiter, ftol, iprint, disp, eps, callback, finite_diff_rel_step, **unknown_options)
    410     g = append(sf.grad(x), 0.0)
    411     c = _eval_constraint(x, cons)
--> 412     a = _eval_con_normals(x, cons, la, n, m, meq, mieq)
    413 
    414     while 1:

~\anaconda3\lib\site-packages\scipy\optimize\slsqp.py in _eval_con_normals(x, cons, la, n, m, meq, mieq)
    484 
    485     if cons['ineq']:
--> 486         a_ieq = vstack([con['jac'](x, *con['args'])
    487                         for con in cons['ineq']])
    488     else:  # no inequality constraint

~\anaconda3\lib\site-packages\scipy\optimize\slsqp.py in <listcomp>(.0)
    484 
    485     if cons['ineq']:
--> 486         a_ieq = vstack([con['jac'](x, *con['args'])
    487                         for con in cons['ineq']])
    488     else:  # no inequality constraint

~\anaconda3\lib\site-packages\scipy\optimize\slsqp.py in cjac(x, *args)
    282                                                  rel_step=finite_diff_rel_step)
    283                     else:
--> 284                         return approx_derivative(fun, x, method='2-point',
    285                                                  abs_step=epsilon, args=args)
    286 

~\anaconda3\lib\site-packages\scipy\optimize\_numdiff.py in approx_derivative(fun, x0, method, rel_step, abs_step, f0, bounds, sparsity, as_linear_operator, args, kwargs)
    424 
    425         if sparsity is None:
--> 426             return _dense_difference(fun_wrapped, x0, f0, h,
    427                                      use_one_sided, method)
    428         else:

~\anaconda3\lib\site-packages\scipy\optimize\_numdiff.py in _dense_difference(fun, x0, f0, h, use_one_sided, method)
    495             x = x0 + h_vecs[i]
    496             dx = x[i] - x0[i]  # Recompute dx as exactly representable number.
--> 497             df = fun(x) - f0
    498         elif method == '3-point' and use_one_sided[i]:
    499             x1 = x0 + h_vecs[i]

TypeError: unsupported operand type(s) for -: 'function' and 'function'

我不知道为什么非评论的cons和评论的cons是不等价的。 谢谢回答！