Numerical Optimization – Details, episodes & analysis

Our mission is to inspire the development of new math research aimed at solving real-world problems. We do this by sharing fun stories behind math formulas and the places they show up.

Stanley Osher is a mathematician at University of California Los Angeles.

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Show Notes:

• Here is the original paper on total variation for denoising.

• Here is a talk from 2003 where Stan describes and shows images from the attack on the truck driver Reginald Denny during the riots in LA (skip to 11:00 for the story).

• Here is the paper on the level set method.

• The company Stan cofounded, Luminescent Technologies, Inc, used the level set method for inverse lithography technology.

• Here is a paper by Candes, Romberg and Tao on compressed sensing, providing rigorous theory for use of the L1 norm.

• An example of "thinking continuously rather than discretely" is the analysis of Su, Boyd, and Candes in providing a short and simple proof for Nesterov acceleration in the continuous setting via a continuous ODE (see Theorem 3 in this ⁠paper⁠).