# Optimization of non-smooth, non-convex, locally Lipschitz functions of type exp(-abs(x))

What would be the numerical method of choice to find minima in a non-smooth, non-convex, locally Lipschitz function $f: \mathbb{R}^n\rightarrow \mathbb{R}$.

The function $f$ is mostly smooth but contains three-dimensional cusps of the following form:
$$g: \mathbb{R}^3\rightarrow \mathbb{R}\\ g(\boldsymbol{x})= -\exp(-{\lVert \boldsymbol x \rVert}_2)$$ with $\lVert \cdot \rVert_2$ being the Euclidean Norm.

• I just tried to minimize the function $g$ that you present using SQP in Python and it converged after 8 iterations. – nicoguaro Feb 7 '17 at 17:12