Disciplined convex programming error：Exponential multiplication

Nonconvex
1

clc
clear all
close all
cvx_begin gp
variables x
object =(1-x)*exp(-x);
maximize object
subject to
0<x<1;
cvx_end
%%%%%%%%%%
Disciplined convex programming error:
Cannot perform the operation: {concave} ./ {log-convex}
%%%%%%%%%%%
Why can’t cvx recognize this form of multiplication?
How can it be solved?

2

Do you see that listed as being allowed in the gp rules http://cvxr.com/cvx/doc/gp.html? I don’t.

Your objective function is concave within your constraint region of 0 < x < 1; so maximization over that domain is inherently a non-convex optimization problem. Actually it is a concave programming problem with compact constraints; therefore, its global maximum occurs at an extreme of the constraints, i.e…, at 0 or 1, and it happens to be at 1.

Your objective function is concave for x > 3, but because it is not concave over the entirety of its natural domain, the prospects for formulating within DCP rules, even if the problem is constrained to x > 3, are not good.

3

How can I solve such problems?
I think CVX does not recognize the expression of the objective function object =(1-x)*exp(-x);

Thank you

4

This is a non-convex problem, which requires a non-convex solver (unless you can solve it by inspection or analytically, as I did with your very simple example). CVX can’t be used for this problem.

Perhaps you need to re-read the Why isn’t CVX accepting my model? READ THIS FIRST FAQ link in my previous answer.

However, essentially of the stuff in https://docs.mosek.com/cheatsheets/conic.pdf can be done in CVX, one way or another. So some multiplicative combinations of x and exp or log are acceptable in certain uses.

5

I am using CVXR to solve a concave objective function. I have a one-dimensional decision variable (x) and the objective function is the summation of 2 natural logarithm terms in which the second term is exponential with different bases of “a and b” (e.g., a^x, b^x) where “a, b” are constants and x is my decision variable. My full objective function is: (-x*sum(ln(y))) + ln((1-x)/((a^(1-x))-(b^(1-x)))) where y is a given 1-D vector of data.

I can successfully code the first term, but I keep getting “Error in xmax^(1 - alpha): non-numeric argument to binary operator” when I add the second term having (a^x and b^x) to the objective. Here is my code:

library(CVXR)
a <- 7
b <- 0.3
M=1000
x_i # is a given vector of 1-D data

x <- Variable(1)
nominator <- (1-x)
denominator <- (1/((a^(1-x))-(b^(1-x))))
obj <- (-xsum(log(x_i)) + Mlog(nominator/denominator)) # change M to the length of X_i later
constr <- list(x>0)
prob <- Problem(Maximize(obj), constr)
result <- solve(prob)
alpha_hat <- result$getValue(x)

I truly appreciate if you can help me with this and tell me what I am doing wrong.
Thanks in advance.

6

CVXR,is a CVX-inspired package running under R, that is a different tool than CVX, which runs under MATLAB, and is the subject of this forum. It is kind of confusing that CVX’s website is at the domain cvxr.com (which predates the CVXR package).

Per the CVXR FAQ at https://cvxr.rbind.io/cvxr_faq/#gen-help

  1. Where can I go for help?

Please post questions to the cvx tag on StackOverflow.

It’s interesting that there is just a “generic” cvx tag at Stack Overflow, rather than one specific to CVXR, but that’s what the CVXR FAQ says, so follow those instructions.

7

Ohh… thanks for letting me know. I posted my question in StackOverflow :>