# The constraint is the sum of infinite terms, and the sum of infinite terms contains optimization variables

When I express this constraint in CVX, most of the Matlab functions say that the input must be a real number, and I can’t convert the CVX variable, hopefully it can give me an idea, thanks!

x_k should be declared as a CVX variable. Everything other than x_k should be input data to CVX, o.e., have double precision value.

I believe all the p_{k,m} will be positive. Therefore, if the sum is truncated to some finite number of terms, it will be convex, and directly enterable into CVX. There is an additional term on the left-hand side which is an exponential of 2*x_k. and another term which affine in the variable x_k, so they can also be entered as in in CVX.

Therefore, the only difficulty is that you will have to truncate the sum at some finite number of terms. Whether that truncation makes the constraint meaningful for your purposes is for you to decide. Whether using a Taylor series expansion, as your formulation works well for your optimization problem, is for you to determine. If you intend to use this in some sort of SCA (Successive Convex Approximation) , good luck, because you’ll probably need it.

First of all, thank you for your quick reply to my question and the solution you provided me, and secondly, the reason why I ask this question is because I am doing a reproduction of a paper, the truncation of finite terms is not ideal, if you take infinite terms, using the symsum function of matlab to nest the gammainc function or nesting the function containing integral that you rewrite yourself, it will show that the input must be a real number. Therefore, I would like to understand if there is a better way to make the upper bound infinite, or only a finite term truncated, this paper ‘‘Computation Offloading Outage Probability Analysis and Min-Max Fairness Optimization in RIS-Assisted MEC System’’ was published by Liang Jin, Xiaodong Xu, et al

You can’t have an explicit infinite sum of terms involving CVX variables or expressions. How to truncate is for you to determine, and has nothing to do with CVX.