log(1+x/y) is a kind of formation of Information entropy，and my obj function is concave. Is there any ways to rewrite this object function ? Thank you.

Well,This is a problem. I just don’t know what kind of expression it should be converted into.And x-1000*log(1+0.01*x*inv_pos(x+1)) reported another error：

Cannot perform the operation: {positive constant} ./ {real affine}

All I know is that my expression is equivalent to yours and conic representable. I’m not sure it implies it also works in cvx but if not it should be only a matter of me making a syntax error.

@Michal_Adamaszek 's solution is correct, and is accepted and solved by CVX.

cvx_begin
variable x
minimize(x-1000*log(1.01-0.01*inv_pos((x+1))))
subject to
x>0
cvx_end

@04014540 Can you show us the complete program you ran which triggered the error message Cannot perform the operation: {positive constant} ./ {real affine} ?

Sorry,I just found my mistake.@Michal_Adamaszek 's solution is right.Thank you so much and I can use a model that similar to this to solve the problem about Information entropy.Best wish to you.

Good afternoon. I have met a relevant about Information entropy question like log(1+1/x)<a. Would you mind send your problem and the corresponding solution to me? It might be a great honor for me to receive your reply. Many thanks!

where t is optimization variable and t <=T and alpha, beta and gamma >0 and real number.
how can rewrite T * log (1+a *x / (b + g *x)) in cvx?
for b and g in the de-numerator, I can’t use the same method

Your remaining piece looks something like log(1+0.01*x/(x+1)) . Make the necessary adaptation. It’s your problem, so you should put in at least some of the effort.

I can’t use this method because I can’t reform the de-numerator to (1+x)
i know a *x / (b + g *x) is can be concave and convex in the domain and DCP can’t perform what is… and I must use inv_pos(.) to define for DCP.
i used a x * inv_pos(b + g * x) but give :Cannot perform the operation: {real affine} . {convex}
i think a *x term must import to inv_pos() function or rewrite a *x / (b + g *x) as affine function for t and use inv_pos() but I can’t…