報告主題：A block symmetric Gauss-Seidel decomposition theorem for convex quadratic programming and its applications (塊對稱高斯-塞得分解定理在凸二次規劃中的應用)
報告人：Kim-Chuan Toh 教授（新加坡國立大學數學系）
會議ID：302 840 008
報告摘要：For a multi-block convex composite quadratic programming (CCQP) with an additional nonsmooth term in the first block, we present a block symmetric Gauss-Seidel (sGS) decomposition theorem, which states that each cycle of the block sGS method is equivalent to solving the CCQP with an additional proximal term constructed from the sGS decomposition of the quadratic term. As a basic building block, the sGS decomposition theorem has played a key role in various recently developed algorithms such as the inexact proximal ALM/ADMM for linearly constrained multi-block convex composite conic programming. We demonstrate how our sGS-based ADMM can be applied to solve doubly nonnegative semidefinite programming and Wasserstein barycenter problems.