I got confused when you changed from `alph*exp(x/sigma)`

in your initial post to `alph*(1-exp(Phi*m/sigma)))`

in your later post, and I mindlessly copy and pasted the latter which is concave, while thinking of the former, which is convex.

I am confused as to what problem you are really trying to solve. You keep switching between `alph*exp(x/sigma)`

and `alph*(1-exp(Phi*m/sigma)))`

. You are not allowed to maximize a convex objective function (unless it is also convex, i.e., affine) in CVX. You either need all 3 terms to separately be convex, or if two of the terms are convex and one is concave, but their sum is convex, reformulate such that there are no concave additive terms.

So if you want

minimize`(1st_term + 2nd_term + alph*(1-exp(Phi*m/sigma)))`

the only way to do so in CVX is if `1st_term + 2nd_term - exp(Phi*m/sigma))`

is convex, in which case you will have to find a reformulation which does not have a concave additive term. Note that I ignored the `+alph`

term because it is a constant, so does not affect the argmin.