Low-Rank Semidefinite Programming: Theory and Applications

Alex Lemon,Anthony Man-Cho So,Yinyu Ye

Low-Rank Semidefinite Programming: Theory and Applications
Format
Paperback
Publisher
now publishers Inc
Country
United States
Published
4 August 2016
Pages
180
ISBN
9781680831368

Low-Rank Semidefinite Programming: Theory and Applications

Alex Lemon,Anthony Man-Cho So,Yinyu Ye

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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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