Scalable Semidefinite Programming

Understand

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.