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LANS Seminar
March 23, 2022 @ 10:30 - 11:30 CDT
Seminar Title: Scalable Semidefinite and Polynomial Optimization via Matrix Decomposition
Speaker: Yang Zheng, Assistant Professor, Electrical and Computer Engineering, University of California, San Diego
Date/Time: March 23, 2022 / 10:30 am – 11:30 am
Location: See meeting URL on the cels-seminars website (requires Argonne login)
Host: Prassana Balprakash
Description: Semidefinite and sum-of-squares (SOS) optimization are two types of convex optimization problems, which have found a wide range of applications in control theory, fluid dynamics, machine learning, and power systems. They can be solved in polynomial-time using interior-point methods in theory, but these methods are only practical for small- to medium-sized instances. In this talk, I will introduce matrix decomposition methods for semidefinite and SOS optimization, which scale more favorably to large-scale problem instances. In the first part, I will apply chordal decomposition to reformulate a sparse semidefinite program (SDP) into an equivalent SDP with smaller PSD constraints that is suitable for the application of first-order methods. The resulting algorithms have been implemented in the open-source solver CDCS. In the second part, I will extend the classical chordal decomposition to the case of sparse polynomial matrices that are positive (semi)definite globally or locally on a semi-algebraic set. The extended decomposition results can be viewed as sparsity-exploiting versions of the Hilbert-Artin, Reznick, Putinar, and Putinar-Vasilescu Positivstellensätze. They allow for much more efficient computations for sparse problems. This talk is based on our work: https://arxiv.org/abs/1707.05058, and https://arxiv.org/abs/2007.11410
Please note that the meeting URL for this event can be seen on the cels-seminars website, which requires an Argonne login.