4
$\begingroup$

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.

$\endgroup$
1
  • 2
    $\begingroup$ I just tried to minimize the function $g$ that you present using SQP in Python and it converged after 8 iterations. $\endgroup$
    – nicoguaro
    Feb 7, 2017 at 17:12

1 Answer 1

3
$\begingroup$

I think I found the right article myself:

Lewis, A.S. & Overton, M.L. Math. Program. (2013) 141: 135. doi:10.1007/s10107-012-0514-2

$\endgroup$
1
  • 1
    $\begingroup$ Yes, that is exactly the right approach: non-smooth Newton methods. $\endgroup$ Feb 8, 2017 at 0:42

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.