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Learn about scalable semidefinite programming in this lecture by Joel Tropp from the California Institute of Technology, presented at IPAM's Statistical and Numerical Methods for Non-commutative Optimal Transport Workshop. Discover a provably correct randomized algorithm for solving large, weakly constrained SDP problems that reduces storage and arithmetic costs. Explore applications including MaxCut relaxations, abstract phase retrieval, and quadratic assignment problems, with demonstrations of the algorithm handling matrix variables containing over 10^14 entries on standard laptop hardware. Understand the key insights behind the algorithm, including problem formulation, bespoke optimization methods, and randomized matrix computations. This presentation is based on collaborative work with Alp Yurtsever, Olivier Fercoq, Madeleine Udell, and Volkan Cevher, referencing research published in SIMODS 2021 and other papers from AISTATS 2017 and NeurIPS 2017.
