How to deal with the erf function in optimization problem?

The following is my problem,

where erf is error function or Gauss error function, and image . Anyone can tell me how to deal with erf fucntion?

Your difficulties extend beyond erf. CVX does have log_normcdf(x), which approximates the cumulative standard Normal distribution function, into which erf is convertible`. However, the variable product stuff going on looks like a total no-go. I don’t think CVX is the tool for this problem.

How obout alternative optimization method to this problem?

You can use a non-convex solver, for instance under YALMIP.

Or you can change this problem into some other non-equivalent (i.e., different argmax) problem. If that problem is convex (see link in my previous post), there might be hope to enter it exactly or approximately into CVX.

ok,thank you. I have another question to ask you,image , if this expression is convex with respect to N?

No. It appears you haven’t read or fully appreciated the link in my previous post.