Example problem using log atom does not converge within maxiter

[cvxpy]

Example problem using log atom does not converge within maxiter

[echu]

Travis,

Do you happen to know what the optimal objective value is? I've increased
the maxiters for cvxopt and it seems to solve it, but I'm not sure if it's
accurate.

Eric

On Tue, Nov 5, 2013 at 1:23 AM, Travis Erdman [email protected]:

The code below (feel free to use it as a test case or example problem)
calculates the maximum expected log return for investment in 10 different
assets with 10 different outcome scenarios. The objective is similar to
that of acent.py, but it is a weighted sum of logs. The solvers do not
converge to the solution within maxiter, though it is a rather
straightforward problem. Any ideas?

import cvxpy as cvx
import cvxopt

scenario_probabilities = cvx.numpy.array((0.3,0.15,0.1,0.1,0.06,0.06,0.06,0.06,0.06,0.05)).reshape(1,-1)
joint_returns = cvx.numpy.array(
[[ 1.09, 0.96, 0.95, 1.06, 1.09, 1.54, 1.16, 1.01, 0.82, 1.04],
[ 1.14, 1.02, 1.04, 1.07, 1.02, 0.93, 1.09, 0.85, 1.47, 1.21],
[ 1.01, 1.35, 0.95, 0.81, 1.05, 0.85, 1.02, 0.88, 1. , 1.05],
[ 1.1 , 0.96, 1.13, 1.95, 1.06, 0.81, 1.02, 1.12, 0.95, 0.97],
[ 1.12, 0.9 , 1. , 1.08, 1.1 , 1.07, 1.7 , 0.94, 0.97, 0.93],
[ 1.64, 1.01, 1.25, 0.97, 0.93, 1.03, 0.81, 1.13, 1.02, 0.91],
[ 0.85, 0.95, 0.98, 0.99, 1.1 , 1.02, 1.04, 1.67, 0.96, 0.96],
[ 1.15, 0.97, 1.54, 0.95, 1.09, 1.14, 1.08, 0.9 , 0.91, 0.82],
[ 1.13, 0.95, 1.1 , 1.03, 1.89, 1.2 , 0.97, 1.04, 1.04, 1. ],
[ 0.93, 1.08, 0.84, 0.97, 0.95, 0.8 , 0.95, 0.98, 1.29, 1.46]])

portfolio = cvx.Variable(10)
riskfree = cvx.Variable()
scenario_returns = riskfree + joint_returns.T * portfolio
objective = scenario_probabilities * cvx.log(scenario_returns)
p = cvx.Problem(cvx.Maximize(objective),[scenario_returns >= 1e-5, riskfree + sum(portfolio) <= 1])

p.solve()

—
Reply to this email directly or view it on GitHubhttps://github.com/cvxgrp/cvxpy/issues/21
.

[echu]

The log atom uses a different solver under the hood. It uses the cvxopt cpl solver. So you can change maxiters using

import cvxopt.solvers as cvxopt
solvers.options["maxiters"] = 1000

Or your favorite maxiters.

Eric

On Nov 5, 2013, at 10:29 AM, Travis Erdman [email protected] wrote:

Yes, the problem and solution are given on p. 1122 of the paper "A Strategy
Which Maximizes the Geometric Mean Return on Portfolio Investments" by
Vander Weide et al.

http://www.albany.edu/faculty/faugere/PhDcourse/GeomeanReturn.pdf

Per the paper, exp(objective.value) should be ~ 1.662; objective.value
should be ~ 0.508.

I tried to do a thorough search for increasing maxiter, but couldn't find
out how to do it.

On Tue, Nov 5, 2013 at 9:13 AM, Eric Chu [email protected] wrote:

Travis,

Do you happen to know what the optimal objective value is? I've increased
the maxiters for cvxopt and it seems to solve it, but I'm not sure if it's
accurate.

Eric

On Tue, Nov 5, 2013 at 1:23 AM, Travis Erdman [email protected]:

The code below (feel free to use it as a test case or example problem)
calculates the maximum expected log return for investment in 10
different
assets with 10 different outcome scenarios. The objective is similar to
that of acent.py, but it is a weighted sum of logs. The solvers do not
converge to the solution within maxiter, though it is a rather
straightforward problem. Any ideas?

import cvxpy as cvx
import cvxopt

scenario_probabilities =
cvx.numpy.array((0.3,0.15,0.1,0.1,0.06,0.06,0.06,0.06,0.06,0.05)).reshape(1,-1)

joint_returns = cvx.numpy.array( \
[[ 1.09, 0.96, 0.95, 1.06, 1.09, 1.54, 1.16, 1.01, 0.82, 1.04], \
[ 1.14, 1.02, 1.04, 1.07, 1.02, 0.93, 1.09, 0.85, 1.47, 1.21], \
[ 1.01, 1.35, 0.95, 0.81, 1.05, 0.85, 1.02, 0.88, 1. , 1.05], \
[ 1.1 , 0.96, 1.13, 1.95, 1.06, 0.81, 1.02, 1.12, 0.95, 0.97], \
[ 1.12, 0.9 , 1. , 1.08, 1.1 , 1.07, 1.7 , 0.94, 0.97, 0.93], \
[ 1.64, 1.01, 1.25, 0.97, 0.93, 1.03, 0.81, 1.13, 1.02, 0.91], \
[ 0.85, 0.95, 0.98, 0.99, 1.1 , 1.02, 1.04, 1.67, 0.96, 0.96], \
[ 1.15, 0.97, 1.54, 0.95, 1.09, 1.14, 1.08, 0.9 , 0.91, 0.82], \
[ 1.13, 0.95, 1.1 , 1.03, 1.89, 1.2 , 0.97, 1.04, 1.04, 1. ], \
[ 0.93, 1.08, 0.84, 0.97, 0.95, 0.8 , 0.95, 0.98, 1.29, 1.46]])

portfolio = cvx.Variable(10)
riskfree = cvx.Variable()
scenario_returns = riskfree + joint_returns.T * portfolio
objective = scenario_probabilities * cvx.log(scenario_returns)
p = cvx.Problem(cvx.Maximize(objective),[scenario_returns >= 1e-5,
riskfree + sum(portfolio) <= 1])

p.solve()

—
Reply to this email directly or view it on GitHub<
https://github.com/cvxgrp/cvxpy/issues/21>
.

—
Reply to this email directly or view it on GitHubhttps://github.com/cvxgrp/cvxpy/issues/21#issuecomment-27792365
.

—
Reply to this email directly or view it on GitHub.

[erdman]

Yes, the problem and solution are given on p. 1122 of the paper "A Strategy
Which Maximizes the Geometric Mean Return on Portfolio Investments" by
Vander Weide et al.

http://www.albany.edu/faculty/faugere/PhDcourse/GeomeanReturn.pdf

Per the paper, exp(objective.value) should be ~ 1.662; objective.value
should be ~ 0.508.

I tried to do a thorough search for increasing maxiter, but couldn't find
out how to do it.

On Tue, Nov 5, 2013 at 9:13 AM, Eric Chu [email protected] wrote:

Travis,

Do you happen to know what the optimal objective value is? I've increased
the maxiters for cvxopt and it seems to solve it, but I'm not sure if it's
accurate.

Eric

On Tue, Nov 5, 2013 at 1:23 AM, Travis Erdman [email protected]:

The code below (feel free to use it as a test case or example problem)
calculates the maximum expected log return for investment in 10
different
assets with 10 different outcome scenarios. The objective is similar to
that of acent.py, but it is a weighted sum of logs. The solvers do not
converge to the solution within maxiter, though it is a rather
straightforward problem. Any ideas?

import cvxpy as cvx
import cvxopt

scenario_probabilities =
cvx.numpy.array((0.3,0.15,0.1,0.1,0.06,0.06,0.06,0.06,0.06,0.05)).reshape(1,-1)

joint_returns = cvx.numpy.array(
[[ 1.09, 0.96, 0.95, 1.06, 1.09, 1.54, 1.16, 1.01, 0.82, 1.04],
[ 1.14, 1.02, 1.04, 1.07, 1.02, 0.93, 1.09, 0.85, 1.47, 1.21],
[ 1.01, 1.35, 0.95, 0.81, 1.05, 0.85, 1.02, 0.88, 1. , 1.05],
[ 1.1 , 0.96, 1.13, 1.95, 1.06, 0.81, 1.02, 1.12, 0.95, 0.97],
[ 1.12, 0.9 , 1. , 1.08, 1.1 , 1.07, 1.7 , 0.94, 0.97, 0.93],
[ 1.64, 1.01, 1.25, 0.97, 0.93, 1.03, 0.81, 1.13, 1.02, 0.91],
[ 0.85, 0.95, 0.98, 0.99, 1.1 , 1.02, 1.04, 1.67, 0.96, 0.96],
[ 1.15, 0.97, 1.54, 0.95, 1.09, 1.14, 1.08, 0.9 , 0.91, 0.82],
[ 1.13, 0.95, 1.1 , 1.03, 1.89, 1.2 , 0.97, 1.04, 1.04, 1. ],
[ 0.93, 1.08, 0.84, 0.97, 0.95, 0.8 , 0.95, 0.98, 1.29, 1.46]])

portfolio = cvx.Variable(10)
riskfree = cvx.Variable()
scenario_returns = riskfree + joint_returns.T * portfolio
objective = scenario_probabilities * cvx.log(scenario_returns)
p = cvx.Problem(cvx.Maximize(objective),[scenario_returns >= 1e-5,
riskfree + sum(portfolio) <= 1])

p.solve()

—
Reply to this email directly or view it on GitHub<
https://github.com/cvxgrp/cvxpy/issues/21>
.

—
Reply to this email directly or view it on GitHubhttps://github.com/cvxgrp/cvxpy/issues/21#issuecomment-27792365
.

[erdman]

Thank you, Eric. I'm glad to know how to adjust this for my future work. Examination of the solution indicates that I formulated this problem incorrectly. Correct formulation follows, with expected results in just 8 iterations.

import cvxpy as cvx
import cvxopt

scenario_probabilities = cvx.numpy.array((0.3,0.15,0.1,0.1,0.06,0.06,0.06,0.06,0.06,0.05)).reshape(1,-1)
joint_returns = cvx.numpy.array( \
    [[ 1.09,  0.96,  0.95,  1.06,  1.09,  1.54,  1.16,  1.01,  0.82,  1.04], \
    [ 1.14,  1.02,  1.04,  1.07,  1.02,  0.93,  1.09,  0.85,  1.47,  1.21], \
    [ 1.01,  1.35,  0.95,  0.81,  1.05,  0.85,  1.02,  0.88,  1.  ,  1.05], \
    [ 1.1 ,  0.96,  1.13,  1.95,  1.06,  0.81,  1.02,  1.12,  0.95,  0.97], \
    [ 1.12,  0.9 ,  1.  ,  1.08,  1.1 ,  1.07,  1.7 ,  0.94,  0.97,  0.93], \
    [ 1.64,  1.01,  1.25,  0.97,  0.93,  1.03,  0.81,  1.13,  1.02,  0.91], \
    [ 0.85,  0.95,  0.98,  0.99,  1.1 ,  1.02,  1.04,  1.67,  0.96,  0.96], \
    [ 1.15,  0.97,  1.54,  0.95,  1.09,  1.14,  1.08,  0.9 ,  0.91,  0.82], \
    [ 1.13,  0.95,  1.1 ,  1.03,  1.89,  1.2 ,  0.97,  1.04,  1.04,  1.  ], \
    [ 0.93,  1.08,  0.84,  0.97,  0.95,  0.8 ,  0.95,  0.98,  1.29,  1.46]])

portfolio = cvx.Variable(10)
scenario_returns = joint_returns.T * portfolio
objective = scenario_probabilities * cvx.log(scenario_returns) 
p = cvx.Problem(cvx.Maximize(objective),[sum(portfolio) == 1])

p.solve()