#### Topic: problem with NLP/NSP

Hi,

my name is Ewing and I'm a financial analyst working at a quantitative research group. I use a variety of optimizers to solve all types of problems - the most prevalent of which are constrained versions of the Markowitz portfolio optimization paradigm.

I have quite a fair bit of experience with Matlab but recently migrated to python where I have found open opt to be a great tool.

Recently, I've encountered strange problems with the NLP/NSP objects: simple problems that were completely and quickly solveable in OpenOpt 0.28 have started crashing in newer versions, including 0.31 for no apparent reason.

Here is the code. This is quite simple and the problem could probably be transformed to use another solver but I typically put in many more non-linear constraints which makes NLP/NSP more suited for my purposes. Please note that the same code runs flawlessly and quickly in version 0.28 but there is a very good chance I'm doing something very wrong here.

Thank you so much for your help.

from openopt import NLP

import numpy as np

numAssets = 25

assets = ['Asset_' + str(currentAsset) for currentAsset in range(0, numAssets)]

def objectiveFunction(x, mu, sigma, aversion = 1):

x_ = x.reshape(-1,1)

return float(np.dot(x_.T,mu) - aversion/2 * np.dot(x_.T, np.dot(sigma, x_)))

def objectiveGradient(x, mu, sigma, aversion = 1):

x_ = x.reshape(-1,1)

return mu - aversion * np.dot(sigma, x_)

def nlConstraint(x, sigma, conVal = 0.02):

x_ = x.reshape(-1, 1)

return np.dot(x_.T, np.dot(sigma, x_)) - pow(conVal,2)/21

def nlConstraintGradient(x, sigma, conVal = 0.02):

x_ = x.reshape(-1, 1)

return 2 * np.dot(sigma, x_)

A = np.identity(numAssets)

b = np.tile(0.2, (numAssets,1))

Aeq = np.tile(1.0, (1, len(assets)))

beq = np.array([0.]).reshape(-1,1)

numOpt = 1000

x_init = np.tile(0., (len(assets), 1))

for currentOpt in range(1, numOpt):

print 'Running opt ' + str(currentOpt)

assetReturns = np.random.randn(1000, numAssets) * 0.5*0.05/pow(252,0.5)

currentMu = assetReturns.mean(axis = 0).reshape(-1, 1)*21

currentSigma = np.cov(assetReturns.T)*21

problem = NLP(f = objectiveFunction, x0 = x_init, A = A, b = b, Aeq = Aeq, beq = beq, \

goal = 'max', df = objectiveGradient, ftol = 1e-5, scale = 1, maxIter = 1e5, iprint = 0,\

c = nlConstraint, dc = nlConstraintGradient , contol = 1e-6, maxFunEvals = 1e6)

problem.args.f = (currentMu, currentSigma)

problem.args.c = (currentSigma,)

problem.solve('ralg')

if problem.stopcase == 1:

x_init = problem.xf.reshape(-1, 1)

else:

print "Not feasible"

break