Low-Rank Semidefinite Programming
Theory and Applications
Seiten
2016
now publishers Inc (Verlag)
978-1-68083-136-8 (ISBN)
now publishers Inc (Verlag)
978-1-68083-136-8 (ISBN)
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. The book then presents applications of the theory to trust-region problems and signal processing.
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.
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.
1: Introduction
PART I THEORY 2: Exact Solutions and Theorems about Rank
3: Heuristics and Approximate Solutions
PART II APPLICATIONS
4: Trust-Region Problems
5: QCQPs with Complex Variables
Appendices A, B, C
References
Erscheinungsdatum | 11.07.2016 |
---|---|
Reihe/Serie | Foundations and Trends® in Optimization |
Verlagsort | Hanover |
Sprache | englisch |
Maße | 156 x 234 mm |
Gewicht | 262 g |
Themenwelt | Mathematik / Informatik ► Informatik ► Theorie / Studium |
Technik ► Elektrotechnik / Energietechnik | |
ISBN-10 | 1-68083-136-4 / 1680831364 |
ISBN-13 | 978-1-68083-136-8 / 9781680831368 |
Zustand | Neuware |
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