Hi All,
Is the function f(x,y,z) = y*log(1+(c*x/(y*z))) is concave ? If so, how can I implement it in cvx (using rel_entr)?
with x,y,z>=0
f(x,y,z) is neither convex nor concave. For instance, at x = y = z = 1, its Hessian has 2 negative eigenvalues and 1 positive eigemvalue, so is indefinite there.
If z were a constant, not a (CVX) variable, f could be expressed as -rel_entr(y,y+c*x/z) and would be concave as a function of x and y.
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