Phase transitions in semidefinite relaxations

Abstract

Modern data analysis requires solving hard optimization problems with a large number of parameters and a large number of constraints. A successful approach is to replace these hard problems by surrogate problems that are convex and hence tractable. Semidefinite programming relaxations offer a powerful method to construct such relaxations. In many instances it was observed that a semidefinite relaxation becomes very accurate when the noise level in the data decreases below a certain threshold. We develop a new method to compute these noise thresholds (or phase transitions) using ideas from statistical physics.

Document Details

Document Type
Pub Defense Publication
Publication Date
Mar 21, 2016
Source ID
10.1073/pnas.1523097113

Entities

People

  • Adel Javanmard
  • Andrea Montanari
  • Federico Ricci-tersenghi

Organizations

  • Air Force Office of Scientific Research
  • Istituto Nazionale di Fisica Nucleare
  • National Science Foundation
  • Sapienza University of Rome
  • Stanford University
  • University of Southern California

Tags

Readers

  • Acoustics.
  • Distributed Systems and Data Platform Development
  • Operations Research