Low-Rank Semidefinite Programming

Theory and Applications
1. Auflage 2016
ISBN: 978-1-68083-136-8
Verlag: Now Publishers

Buch, Englisch, Band 5, 178 Seiten, Format (B × H): 156 mm x 234 mm

Reihe: Foundations and Trends® in Optimization

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.

Autoren/Hrsg.

Lemon, Alex

So, Anthony Man-Cho

Ye, Yinyu

Fachgebiete

• Technische Wissenschaften Elektronik | Nachrichtentechnik Nachrichten- und Kommunikationstechnik Signalverarbeitung
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Optimierung
• Mathematik | Informatik Mathematik Operations Research

Inhaltsverzeichnis

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.