How does the subtraction of two log functions conform to the DCP rule?

hello,I have a problem about object’s like log(1+A/B), it’s a convex function.And I want to translate it to Log(A+B)-Log(B).
But this is convex-convex,it doesn’t fit DCP rules.How should i solve it? Thank you !

Show us exactly the function you claim to be convex. log(1+A/B)is not convex (or concave) if A and B are both optimization variables.

Thank you! I have read it. My function is f(x, y) = log(1+A/(H^2 + (x-x0).^2 + (y-y0).^2 + B)).All of them are constants except for x and y. Optimization variables only are x and y.

You have read it? Then where’s your convexity proof?

Let A = 1, H = x0 = y0 = B = 0. That results in the simplified function log(1+1/(x^2+y^2)). Its Hessian evaluated at x = y = 1 has one negative eigenvalue and one positive eigenvalue. Therefore, the function is neither convex nor concave, and can’t be used in CVX.

Thank you! In your example this function is really not convex.I’ll check my problem again.Thank you for your answer. Best wishes to you.

the expression just like the SNR, right?When you mention the form as log-log ,It reminds me of causal constraints,if you want to deal with the expression as f(x,y),you should use SCA(successive convex approximate) to turn it into a reasonable form,if you want to deal with log-log,This is clearly an illegal form,maybe you should use slack variable。

yes, you’re right.In fact, I had used SCA and slack variable.I set slack variable S = (x-x0).^2 + (y-y0).^2.
so this function can translate into a convex function respect to S.Thanks for your answer.