How to solve the objective function in images with cvx?
in the objective function can be entered into CVX using a first-order Taylor expansion.
is a concave function that is fed into CVX and keeps reporting the error log(convex ).It looks like the objective and the last two constraints are non-convex.
The objective consists of {log-sum-inv} - {log-sum-inv}, which is{convex} - {convex}. There are plenty of posts on this forum for how to deal with log-sum-inv. But the first term is a convex term which is being maximized, which is a non-convex operation. So that makes this a non-convex problem, unless somehow the input data is such that it allows a simplification into a concave objective (being maximized).
The last two constraints appear to have quadratic functions of a variable on the wrong side of the inequality to be convex.
Dear Mark_L_Stone,
I agree with your point about the first term of the objective function being a convex function, but that is I can use the first order Taylor expansion to approximate that expression as a linear function with respect to the optimization variables, and the transformed linear function can be considered as a concave function in the domain of definition that can be maximized.
The function 
is convex.
The function
is concave,due to the “-”.
According to the convexity-preserving operation, since is a concave function,
add a linear function must be a concave function, and it can be maximized.
My question now is how to use cvx to express equivalently.
You can search on this forum for log-sum-inv to see how to handle that.
That still doesn’t address the non-convex constraints.
