Scalable Semidefinite Programming
Abstract
Semidefinite programming (SDP) is a powerful framework from convex optimization that has striking potential for data science applications. This paper develops a provably correct randomized algorithm for solving large, weakly constrained SDP problems by economizing on the storage and arithmetic costs. Numerical evidence shows that the method is effective for a range of applications, including relaxations of MaxCut, abstract phase retrieval, and quadratic assignment. Running on a laptop equivalent, the algorithm can handle SDP instances where the matrix variable has over $10^{14}$ entries.
- Publication:
-
arXiv e-prints
- Pub Date:
- December 2019
- DOI:
- 10.48550/arXiv.1912.02949
- arXiv:
- arXiv:1912.02949
- Bibcode:
- 2019arXiv191202949Y
- Keywords:
-
- Mathematics - Optimization and Control;
- Mathematics - Combinatorics;
- 90C22;
- 65K05 (Primary);
- 65F99 (Secondary)
- E-Print:
- SIAM Journal on Mathematics of Data Science, vol. 3, num. 1, pp. 171-200, Feb. 2021