non-linear convex problem with sensitivity issue

[sl]

Hi,

I am trying to solve a non-linear optimization problem and hitting some data sensitivity issue. Here is a simplified version that already shows the problem; of course I don't have to use log for this simple setup itself but I need it in the more general setup:

Given [r0,r1], find [w0,w1] such that it

    minimize -log(1+ r0*w0 + r1*w1)

    subject to w0>=0, w1>=0, w0+w1<=1.0, and -log(1+ r0*w0 + r1*w1)<=-log(0.9)

so

    f0 = -log(1+ r0*w0 + r1*w1)

    f1 = f0+ log(0.9) 

If (r0,r1) is (-0.2,0.1), the solver finds the optimal solution (0,1); but if I change to (-0.4,1), it gets stuck; in fact all the points fed into F are zeros.

Here is the code... can some one please help? Thanks..

from cvxopt import matrix, solvers

import numpy as np

import math

import cvxopt

r=matrix([-0.4, 0.1]).T

def F(w=None, y=None):

    if w is None: return (1, matrix(0.0, (2,1)))

    if min(w)<0 or sum(w)>1.0: return None

 

    f=matrix(0.0, (2,1))

    Df=matrix(0.0, (2,2))

    z= (1.0+ r*w)[0,0]

    f[0,0]= -math.log(z)

    Df[0,:]= - r/z

    f[1,0]= math.log(0.9)-f[0,0]

    Df[1,:]= Df[0,:]

    if y is None: return f,Df

    H=y[0]* r.T*r/(z*z) + y[1]*r.T*r/(z*z)

    return f,Df,H

G=matrix(0.0, (3,2))

h=matrix(0.0, (3,1))

G[0:2,:]=-matrix(np.identity(2))

G[2,:]= matrix(1.0, (1,2))

h[2]= 1.0

sol=solvers.cp(F, G, h)

print(sol['x'])

[sl]

There was a small typo in the code but it did not make much of difference...

from cvxopt import matrix, solvers

import numpy as np

import math

import cvxopt

r=matrix([-0.4, 0.1]).T

def F(w=None, y=None):

    if w is None: return (1, matrix(0.0, (2,1)))

    if min(w)<0 or sum(w)>1.0: return None

 

    f=matrix(0.0, (2,1))

    Df=matrix(0.0, (2,2))

    z= (1.0+ r*w)[0,0]

    f[0,0]= -math.log(z)

    Df[0,:]= - r/z

    f[1,0]= math.log(0.9)+f[0,0]