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Low-Rank Semidefinite Programming : Theory and Applications, Paperback / softback Book

Low-Rank Semidefinite Programming : Theory and Applications Paperback / softback

Part of the Foundations and Trends (R) in Optimization series

Paperback / softback

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Finding low-rank solutions of semidefinite programs is important in many applications.

For example, semidefinite programs that arise as relaxations of polynomial optimization problems are exact relaxations when the semidefinite program has a rank-1 solution.

Unfortunately, computing a minimum-rank solution of a semidefinite program is an NP-hard problem. This monograph reviews the theory of low-rank semidefinite programming, presenting theorems that guarantee the existence of a low-rank solution, heuristics for computing low-rank solutions, and algorithms for finding low-rank approximate solutions.

It then presents applications of the theory to trust-region problems and signal processing.

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