具有非线性约束的科学最小化

如何解决具有非线性约束的科学最小化

我正在尝试优化此模型：

最小化obj：sum（变量* a）

s.t：1）sum（log（变量）* c）> = b

1. sum（variables）= 1

2. 变量> = 0

其中'a'和'b'是常数，'c'是类型概率的向量。我尝试了scipy包中的三种不同方法，但是没有一种有效。这是我使用'trust-constr'方法的代码

def objective(x):
    return np.sum(np.dot(x,v))

lincos = LinearConstraint( [1]*(len(f)),1,1)
lincos1 = LinearConstraint( [1]*(len(f)),np.inf)
nonlincos = NonlinearConstraint(constraint,0.01,np.inf)

result1 = minimize(objective,f,method='trust-constr',constraints=[lincos,lincos1,nonlincos ] )

这给出了一个值错误，在该值以下，我认为这与我的日志约束有关，但我不知道该如何解决。

............................................... .................................

ValueError                                Traceback (most recent call last)
<ipython-input-97-18fbd5e75692> in <module>
----> 1 result1 = minimize(objective,nonlincos ] )

~\Anaconda3\lib\site-packages\scipy\optimize\_minimize.py in minimize(fun,x0,args,method,jac,hess,hessp,bounds,constraints,tol,callback,options)
    620         return _minimize_trustregion_constr(fun,621                                             bounds,--> 622                                             callback=callback,**options)
    623     elif meth == 'dogleg':
    624         return _minimize_dogleg(fun,~\Anaconda3\lib\site-packages\scipy\optimize\_trustregion_constr\minimize_trustregion_constr.py in _minimize_trustregion_constr(fun,grad,xtol,gtol,barrier_tol,sparse_jacobian,maxiter,verbose,finite_diff_rel_step,initial_constr_penalty,initial_tr_radius,initial_barrier_parameter,initial_barrier_tolerance,factorization_method,disp)
    517             initial_barrier_tolerance,518             initial_constr_penalty,--> 519             factorization_method)
    520 
    521     # Status 3 occurs when the callback function requests termination,~\Anaconda3\lib\site-packages\scipy\optimize\_trustregion_constr\tr_interior_point.py in tr_interior_point(fun,lagr_hess,n_vars,n_ineq,n_eq,constr,fun0,grad0,constr_ineq0,jac_ineq0,constr_eq0,jac_eq0,stop_criteria,enforce_feasibility,state,initial_tolerance,initial_penalty,initial_trust_radius,factorization_method)
    327             constr0_subprob,jac0_subprob,subprob.stop_criteria,328             state,trust_radius,--> 329             factorization_method,trust_lb,trust_ub,subprob.scaling)
    330         if subprob.terminate:
    331             break

~\Anaconda3\lib\site-packages\scipy\optimize\_trustregion_constr\equality_constrained_sqp.py in equality_constrained_sqp(fun_and_constr,grad_and_jac,constr0,jac0,scaling)
    119         dt,cg_info = projected_cg(H,c_t,Z,Y,b_t,120                                    trust_radius_t,--> 121                                    lb_t,ub_t)
    122 
    123         # Compute update (normal + tangential steps).

~\Anaconda3\lib\site-packages\scipy\optimize\_trustregion_constr\qp_subproblem.py in projected_cg(H,c,b,lb,ub,max_iter,max_infeasible_iter,return_all)
    497     # Initial Values
    498     x = Y.dot(-b)
--> 499     r = Z.dot(H.dot(x) + c)
    500     g = Z.dot(r)
    501     p = -g

~\Anaconda3\lib\site-packages\scipy\sparse\linalg\interface.py in dot(self,x)
    413 
    414             if x.ndim == 1 or x.ndim == 2 and x.shape[1] == 1:
--> 415                 return self.matvec(x)
    416             elif x.ndim == 2:
    417                 return self.matmat(x)

~\Anaconda3\lib\site-packages\scipy\sparse\linalg\interface.py in matvec(self,x)
    227             raise ValueError('dimension mismatch')
    228 
--> 229         y = self._matvec(x)
    230 
    231         if isinstance(x,np.matrix):

~\Anaconda3\lib\site-packages\scipy\sparse\linalg\interface.py in _matvec(self,x)
    525 
    526     def _matvec(self,x):
--> 527         return self.__matvec_impl(x)
    528 
    529     def _rmatvec(self,x):

~\Anaconda3\lib\site-packages\scipy\optimize\_trustregion_constr\projections.py in null_space(x)
    191         # v = P inv(R) Q.T x
    192         aux1 = Q.T.dot(x)
--> 193         aux2 = scipy.linalg.solve_triangular(R,aux1,lower=False)
    194         v = np.zeros(m)
    195         v[P] = aux2

~\Anaconda3\lib\site-packages\scipy\linalg\basic.py in solve_triangular(a,trans,lower,unit_diagonal,overwrite_b,debug,check_finite)
    334 
    335     a1 = _asarray_validated(a,check_finite=check_finite)
--> 336     b1 = _asarray_validated(b,check_finite=check_finite)
    337     if len(a1.shape) != 2 or a1.shape[0] != a1.shape[1]:
    338         raise ValueError('expected square matrix')

~\Anaconda3\lib\site-packages\scipy\_lib\_util.py in _asarray_validated(a,check_finite,sparse_ok,objects_ok,mask_ok,as_inexact)
    244             raise ValueError('masked arrays are not supported')
    245     toarray = np.asarray_chkfinite if check_finite else np.asarray
--> 246     a = toarray(a)
    247     if not objects_ok:
    248         if a.dtype is np.dtype('O'):

~\Anaconda3\lib\site-packages\numpy\lib\function_base.py in asarray_chkfinite(a,dtype,order)
    497     if a.dtype.char in typecodes['AllFloat'] and not np.isfinite(a).all():
    498         raise ValueError(
--> 499             "array must not contain infs or NaNs")
    500     return a
    501 

ValueError: array must not contain infs or NaNs