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.
- ISBN13 9781680831368
- Publish Date 4 August 2016
- Publish Status Active
- Publish Country US
- Imprint now publishers Inc
- Format Paperback
- Pages 180
- Language English
- URL https://nowpublishers.com/article/Details/OPT-009