minimize with constraints to solve for coefficients

Question

my objective is to conduct quadratic curve fitting according to y=a*x**2 + b *x+cwith bounds on two variables variables a<0,c<=0 and a constraint 2*a*x+b >=0. In short, I want the fit to be monotonic increasing function in first quadrant with y(x=0) <= 0. My sample code consists of three trials in using scipy.optimize.minimize function:

(1) I don't specify jacobian: works perfect on regular data.

(2) specify jacobian: is not able to predict even on regular data: some issues with jacobian definition.

(3) apply constraint: constrain definition is raising error.

Can I seek your attention to make this program run ?

import numpy as np
from scipy.optimize import minimize

# scattr-irregular
#xip=np.array([ 0.02237461, 0.0983837 , 0.25707382, 0.56959641, 1.33419197, 4.95835927])
#yip=np.array([0.20085822, 0.23583258, 0.28996988, 0.36350284, 0.47981232, 0.67602165] )
#scatter- regular
xip=np.array([2.12E-01,3.43E-01,5.01E-01,7.01E-01,9.73E-01,1.15E+00,1.34E+00,1.41E+00])
yip=np.array([5.94E-02,1.28E-01,2.05E-01,2.90E-01,3.86E-01,4.34E-01,4.78E-01,4.93E-01])

import  matplotlib.pyplot as plt
plt.scatter(xip,yip, label = 'scatter')

xipfit=np.linspace(0, max(xip), 200)

#minimize.scipy
def func(abc,x,y):
    """ Objective function """
    return ((abc[0]*x**2+abc[1]*x**1+abc[2]-y)**2).sum()

def func_deriv(abc, x,y):
    """ Derivative of objective function """
    dfda = 2*(abc[0]*x**2+abc[1]*x**1+abc[2]-y)*x**2
    dfdb = 2*(abc[0]*x**2+abc[1]*x**1+abc[2]-y)*x**1
    dfdc = 2*(abc[0]*x**2+abc[1]*x**1+abc[2]-y)* 1
    return np.array([ dfda.sum(), dfdb.sum(), dfdc.sum() ])  

#2*a*x+b >=0    
cons = ({'type': 'ineq',
         'fun' : lambda abc: np.array( [ 2*abc[0]*xip.sum()+abc[1] ]) ,
         'jac' : lambda abc: np.array([2*xip.sum(),  1,  0])\
         })    
######################################################    
###1. wO jacobian input; works for specific data.    
coeffs_WOjac= minimize(func, x0=[-1.0,1.0,-1], args=(xip,yip),\
                jac=False,\
                method='SLSQP',\
                bounds=((-1e6,0),(0,1e6),(-1e6,0)),\
                options={'disp': True})
yipfit_WOjac = coeffs_WOjac.x[0]*xipfit**2\
                +coeffs_WOjac.x[1]*xipfit \
                +coeffs_WOjac.x[2]
print(coeffs_WOjac)                
plt.plot(xipfit,yipfit_WOjac,label='WOjac', linewidth=4)
######################################################                
###2. wit jacobian input: fit is not correct. jacobain correct ?             
coeffs_Wjac= minimize(func, x0=[-1.0,1.0,-1], args=(xip,yip),\
                jac=func_deriv,\
                method='SLSQP', \
                bounds=((-1e6,0),(-1e6,1e6),(-1e6,0)),\
                options={'disp': True})
yipfit_Wjac = coeffs_Wjac.x[0]*xipfit**2\
                +coeffs_Wjac.x[1]*xipfit \
                +coeffs_Wjac.x[2]
print(coeffs_Wjac)
plt.plot(xipfit,yipfit_Wjac,label='Wjac', color= 'red',linewidth=1.5)
######################################################                
###3. wO jacobian and constraints  
coeffs_WOjac_constr = minimize(func, x0=[-1.0,1.0,-1], args=(xip,yip),\
                jac=False,\
                constraints=cons,\
                method='SLSQP', 
                bounds=((-1e6,0),(-1e6,1e6),(-1e6,0)),\
                options={'disp': True})                
yipfit_WOjac_constr = coeffs_WOjac_constr.x[0]*xipfit**2\
                +coeffs_WOjac_constr.x[1]*xipfit \
                +coeffs_WOjac_constr.x[2]

plt.plot(xipfit,yipfit_WOjac_constr,label='Wjac_constr', linewidth=2)


plt.legend(loc='upper left')
plt.grid()                

I am simultaneously trying to try lmfit capabilities in this post. Hence though of bringing attention to this post as well.

edit: code has been re formatted to un/comment individual method.

edit2:Jacobian is defined correctly.

edit 3: working code. incorporated changes from the comments. deleted xip, yip in the cons subroutine.