Semialgebraic Proofs and Efficient Algorithm Design (Foundations and Trends

by Noah Fleming

In the last two decades a link has been established that, in some cases, proof that a solution exists has enabled an algorithm to find that solution itself. This has had most effect on semialgebraic proof systems and linear and semidefinite programming. This monograph details the interplay between proof systems and efficient algorithm design and surveys the state-of-the-art for two of the most important semi-algebraic proof Sherali-Adams and Sum-of-Squares. It provides the readers with a rigorous treatment of these systems both as proof systems, and as a general family of optimization algorithms. The emphasis is on illustrating the main ideas by presenting a small fraction of representative results with detailed intuition and commentary. The monograph is self-contained and includes a review of the necessary mathematical background including basic theory of linear and semidefinite programming. Semialgebraic Proofs and Efficient Algorithm Design provides the advanced reader with a deep insight into the exciting line of research. It will inspire readers in deploying the techniques in their own further research.

234 pages, Paperback

Published December 10, 2019

About the author

NOAH FLEMING is a strategic marketing expert and CEO of Fleming Consulting & Co. He has provided coaching and consulting services for thousands of business owners, executives, and individuals, and is an expert blogger for FastCompany and guest blogger for The Globe and Mail’s “Report on Business.”