1

I am trying to solve a nonlinear convex optimization problem of the following form c'x + f(x) subject to some affine constraints. Before that I wanted to make sure that I can solve a simple problem without f(x). Since I have the analytical first and second derivative of the problem I want to use them to get faster results. I am trying to use cvxopt to solve the problem. I wrote following code for the problem.

maximize Sum(l*r_i*x_i,i=1:n-1)
s.t.   sum(x_i, i=1:n) =1
       x_i -v_i*x_n<=0 i=1,...,n-1
       0<=x_i<=1

But I cannot achieve optimal solution to this using cvxopt. If I use the modeling functionality of cvxopt, I can solve it easily. But unfortunately, I am not sure if I can provide analytical first and second derivative using that.

Here is the code for the problem

from cvxopt import matrix, log, div, spdiag, solvers, spmatrix
import numpy as np

def F(x=None, z = None):
    m,n = A.size
    if x is None: return 0,matrix(0.5,(n,1))
    if (min(x) <0. or max(x)>1.): return None
    f = matrix(-l*r.T*x[:-1])
    Df = -l*matrix(np.append(r,0)).T
    if z is None: return f,Df
    H = matrix(0.0, (n,n))
    return f,Df,H


dd = 6
l = 19
C = 1.2 * l
theta = 1.25
v = [4.99, 4.66, 3.84, 4.58, 2.54, 1.83]
r = matrix(np.array([max(0.8, 1 - 0.04 * i) for i in range(dd)]))
A = matrix(np.zeros([dd, dd + 1], dtype=float))
for i in range(dd):
    A[i, i] = 1.0
    A[i, -1] = -v[i]
b = matrix(np.zeros([dd, 1], dtype=float))
A_eq = matrix(np.ones([1, dd + 1], dtype=float))
b_eq = matrix([1.0])

solvers.cp(F,G=A,h=b, A= A_eq,b=b_eq).solve()

I am probably making some mistake in this code. Any help or guidance will be greatly appreciated.

deepAgrawal
  • 673
  • 1
  • 7
  • 25
  • I did not check your F, but i highly think there is something wrong within it as the solver-behaviour is strange (increasing it's and iterative-refinement won't help). Your problem looks so simple in math-form, that i highly recommend trying out cvxpy, which has nicer modelling and imho the better solvers (incl. cvxopt, while not beeing that tunable like a-priori KKT-solvers). – sascha Jun 17 '17 at 12:13

0 Answers0