Numerical Optimization – Details, episodes & analysis

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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).

Deanna Needell is a Professor of Mathematics at University of California, Los Angeles (UCLA) and a leading researcher in compressed sensing, numerical linear algebra, data science, and machine learning. Her work has shaped modern sparse recovery and randomized iterative algorithms, and she is widely known for co-developing CoSaMP, a cornerstone method in compressed sensing. More broadly, her research connects linear algebra and optimization with machine learning.

Deanna’s research excellence has been recognized with several honors, including the IMA Prize in Mathematics and its Applications, an NSF CAREER Award, a Sloan Research Fellowship, and election as a Fellow of the American Mathematical Society and a Fellow of SIAM. Beyond theory, Deanna has applied mathematical tools to real-world problems in areas such as imaging, public health, and legal analytics, including work on Lyme disease data and collaborations with organizations like the California Innocence Project. She serves as the Executive Director for the Institute for Digital Research and Education and the Dunn Family Endowed Chair in Data Theory, and is deeply committed to mentorship, inclusiveness, and building bridges between mathematics and society.