I met a problem while using cvx. My objective function is f(x,y) = lb(c+x/y),c>1and c is a constant,x>0,y>0. The function is convex, but I don’t know how to express which in cvx.Example, N2 = log(chanlgain+sigma + derta*(1/rho(k)))/log(2);rho(k) is a variable.
You may find what you need at
@Erling’s reference is a good. one. For the particular case of log(1+1/x) . it can be reformulated in CVX as log(1 + 1/x) = rel_entr(x,x+1) + rel_entr(x+1,x) or -log(1 - inv_pos(1+x)). The first of these reformulations is preferred if CVXQUAD is used (but better to use Mosek if available). These are a little simpler in CVX than the formulation shown in Mosek Conic Modeling Cheatsheet because they take advantage of higher level CVX functions than are assumed in the Cheatsheet.
You can use the reformulation log(c+d/x) = log(1+1/(x*c/d))+log(c) to put it into this form. I.e., use x*c/d in place of x in the reformulations for log(1+1/x) and add log(c).