# Log( {positive convex} )

Continuing the discussion from Status: Unbounded Optimal value (cvx_optval): -Inf:

help cvx/log

``````Disciplined convex programming information:
log(X) is concave and nondecreasing in X. When used in CVX
expressions, X must be concave.``````

Thang you!
my Log is log（(Pbeta/(x+H))+a）,where P, beta ,H and a are 11 constant. how can i edit it with CVX.

Do you know the values or ranges of the constants? Have you proven it is convex?

Is y the only optimization (CVX) variable? if so, the sign of the 2nd derivative w.r.t y will show convexity or not.

when I rewirtten the program as
for n=1:1:N
for k=1:1:K
for m=1:1:M
if m==1
r(n,k,m)=log2((p2beta/(y(n,k,m)+H^2))+delta);
% r(n,k,m)=rel_entr(p2
beta+(y(n,k,m)+H^2)delta,y(n,k,m))+rel_entr(y(n,k,m),p2beta+(y(n,k,m)+H^2)delta);
else
r(n,k,m)=log2((p1
beta/(y(n,k,m)+H^2))+delta);
% r(n,k,m)=rel_entr(p1*beta+(y(n,k,m)+H^2)delta,y(n,k,m))+rel_entr(y(n,k,m),p1beta+(y(n,k,m)+H^2)*delta);
end
end
end
end
Disciplined convex programming error:
Invalid operation: {0.0001} / {real affine}.

However, when i written the program as follow
for n=1:1:N
for k=1:1:K
for m=1:1:M
if m==1
r(n,k,m)=log2((p2betainv_pos(y(n,k,m)+H^2))+delta);
% r(n,k,m)=rel_entr(p2beta+(y(n,k,m)+H^2)delta,y(n,k,m))+rel_entr(y(n,k,m),p2beta+(y(n,k,m)+H^2)delta);
else
r(n,k,m)=log2((p1
beta
inv_pos(y(n,k,m)+H^2))+delta);
% r(n,k,m)=rel_entr(p1*beta+(y(n,k,m)+H^2)delta,y(n,k,m))+rel_entr(y(n,k,m),p1beta+(y(n,k,m)+H^2)*delta);
end
end
end
end
Disciplined convex programming error:
Invalid operation: log( {positive convex} )