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Events by date

Friday, September 18, 2020

Friday, September 18, 2020 — 3:30 PM EDT

Title: Hard Combinatorial Problems, Doubly Nonnegative Relaxations, Facial
and Symmetry Reduction, and Alternating Direction Method of Multipliers

Speaker: Henry Wolkowicz Affiliation: University of Waterloo Zoom: Please email Emma Watson

Abstract:

Semi-definite programming, SDP, relaxations have proven to be extremely successful both in theory and practice for many hard combinatorial problems. This is particularly true for the Max-Cut problem, where problems of dimension in the thousands have been solved to optimality. In contrast, the quadratic assignment problem, QAP, is an NP-hard problem where dimensions bigger than $30$ are still considered hard. SDP and in particular, the doubly nonnegative, DNN, relaxation have been successful in providing strong upper and lower bounds, and even solving many instances to optimality. 

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