Foundations and Trends in Theoretical Computer Science Ser.: Semialgebraic Proofs and Efficient Algorithm Design by Toniann Pitassi, Pravesh Kothari and Noah Fleming (2019, Trade Paperback)
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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 systems: Sherali-Adams and Sum-of-Squares.