Approximate an exponential function

Question

I have an optimization problem, where I would like to minimize $$F=\exp(\mathrm{trace}(A)+\frac{1}{2}\mathrm{trace}(A^2)-\lambda)$$ where $A$ is a non-negative matrix.

Is it possible to replace $F$ with $G=\mathrm{trace}(A)+\frac{1}{2}\mathrm{trace}(A^2)-\lambda$ and minimizes $G$ instead of $F$?

Answer 1

Since $\exp$ is an increasing function, yes, $F$ and $G$ have the same minimizers.

See also my answer here.