How to present my convex optimization in a CVX-compliant way

1

Hello,

I am new to CVX optimization toolbox. Recently, I am trying to solve a convex optimization via CVX in MATLAB, but I get an error stated as follows,

“Disciplined convex programming error:
Cannot perform the operation: {convex} .* {real affine}”

In the following, I give more details to my problem,

fig1.JPG736×374 35.3 KB

fig2.JPG745×466 76.1 KB

Finally, the above error is incurred when expressing the following segment within the objective function,

by

So, I just wonder if it is possible for me to express it in a CVX-compliant way, and if yes, how can I make the adjustment.

Kind regards,
Allan

2

You haven’t offered up any code so it’s unlikely we will be able to help you. If you do post code, please make sure to isolate exactly the line that is causing the problem, and make sure we know which quantities are declared as variables.

3

Hello, Ph.D. Grant,

Thank you for you timely reply. In this message, I would like to make some complement to my original problem, and then attach my MATLAB code for a better trouble-shooting.

After introducing the two auxiliary variables, i.e., ,
the original problem in (1) is transferred into (3) below (please forgive my rashness, I miss a linear constraint in the original form, i.e., (3-b), though it will not affect the concavity of the problem),

The corresponding MATLAB code:

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Error using cvx/times (line 173)
Disciplined convex programming error:
    Cannot perform the operation: {convex} .* {real affine}

Error in cvx/mtimes (line 36)
    z = feval( oper, x, y );

Error in EEMR_sub9>Fun_obj (line 87)
            val_obj=val_obj-q_temp*para_sigma*(d1_temp/c1_temp)*x_var((bb-1)*num_dlk+aa,cc)*inv_pos(1-c1_temp*inv_pos(x_var((bb-1)*num_dlk+aa,cc))*w_var((bb-1)*num_dlk+aa,cc));
4

You haven’t show us what Fun_obj or is; nor do we know exactly where the error is occurring.

5

Hello, Ph.D. Grant,

I have re-edited my reply.

Kind regards,
Allan

6

To make it more clear, the error is incurred by the following codes painted in yellow,

and it corresponds to the following segment within the objective function,

Pasted image718×146 19.7 KB

7

Ah, OK, that’s a pretty hairy product. I am not convinced that is convex as constructed, and I’m far from convinced it can be rendered in CVX even if it is convex. Do read the FAQ including the section “Yes, I’m sure my model is convex!” for an explanation. Perhaps others can show how to reformulate your model.

8

Thanks for your time and explanations, and I guess I will try to resolve the above problem from the dual perspective.