How I can find an optimal solution for a model with concave-convex objective function?

Question

My objective function is sum of three functions, 2 linear functions and a concave function
($1-\exp(x)$); constraints of my model are convex. How can I obtain optimal solution from this problem?

Answer 1

Solve $\Delta f_{vex}(x^{n+1})=-\Delta g_{cave}(x^n)$ where $f_{vex}(.)$ is the convex part, being the sum of the two linear functions and $g_{cave}$ is the concave part and $x^{n}$ denotes the $n^{th}$iterate of the solution. This is also known as the concave-convex procedure.