使用Python中的两个变量优化非线性函数

Question

我正在尝试优化以下功能：

f(x,a+,a-,b) = a+*((1/(1+exp(-b*x)) - 1/2) if x>=0
             = a-*((1/1+exp(-b*x)) -1/2)  if x<0 

constraints: a+ * b <=4, a-*b <=4
             a+/2 <= max(if(x>0))
             a-/2 <= -min(if(x<0))

我试图通过将边界[[0,2），（0,2），（1，None）]和约束定义为上面定义的方式使用最小化函数，但是该函数未提供正确的结果，尤其是如果我使用beta作为约束中的参数时。

from scipy.optimize import minimize 

init_params=[0.0,0.0,20.0]
bnds = [(0.0,2.0), (0.0,2.0), (1.0,None)]
S_curve = pd.DataFrame()
S_curve['year'] = dfs2.index
S_curve['H_Change'] = np.array(dfs2.loc[:,'annualH_chg'])
S_curve['R_Change'] = np.array(dfs2.loc[:,'annualR_chg'])
S_curve['Weight'] = 1
S_curve.reset_index(drop=True)
weighted = S_curve[S_curve.Weight !=0]
minimum = -S_curve['R_Change'].min()
maximum = S_curve['R_Change'].max()
beta=init_params[2]

def constraint1(up, beta):
    return 4.0-(up*beta)

def constraint2(down, beta):
    return 4.0-(down*beta)

def constraint3(up, maximum):
    return maximum - up/2.0

def constraint4(down, minimum):
    return minimum - down/2.0

cons = [{'type':'ineq', 'fun':constraint1, 'args':(beta,)},
        {'type':'ineq', 'fun':constraint2, 'args':(beta,)},
        {'type':'ineq', 'fun':constraint3, 'args':(maximum,)},
        {'type':'ineq', 'fun':constraint4, 'args':(minimum,)}]

soln = minimize(func, init_params, bounds=bnds, constraints=cons, method='SLQSP')

期望满足第一个约束和第二个约束，并且beta（b）不是常数。