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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?

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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.

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