I attempt to solve an optimization which is a sum of two convex functions and one non-convex function described as follows:
$$g(x,y) = a{\log_2}{\left( {1 + x} \right)} + b\log_2 \left[ 1 + c(x - dy) \right] - x(y+e)$$
The two logarithm terms are convex (can prove the convexity using hessian matrix) while the third term in the function $g(x,y)$ is non-convex. Could anyone give me a suggestion to solve this problem? Thanks a lot.