# lipschitz constant of a multivariate function

I have a function $f:\mathbb{R}^{50} \rightarrow \mathbb{R}$ and I need to compute the Lipschitz constant of $f$ to solve an optimization problem using a specific algorithm. Does any one have suggestions on how to estimate such Lipschitz constants?

Suggestions are greatly appreciated. Thanks!

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## 1 Answer

Rather than compute "the" Lipschitz constant, it is much easier to do a backtracking line search that roughly upper-bounds the Lipschitz constant.

To get some ideas, on how one might do a simple line-search, search google for "line search", "backtracking line search" and the ilk, and you'll find several useful ideas.

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