Semidefinite programming (SDP) is a powerful framework from convex optimization that has striking potential for data science applications. This paper develops provably correct randomized algorithm solving large, weakly constrained SDP problems by economizing on the storage and arithmetic costs. Numerical evidence shows method effective range of applications, including relaxations MaxCut, abstra...

An exact semidefinite linear programming (SDP) relaxation of a nonlinear semidefinite programming problem is a highly desirable feature because a semidefinite linear programming problem can efficiently be solved. This paper addresses the basic issue of which nonlinear semidefinite programming problems possess exact SDP relaxations under a constraint qualification. We do this by establishing exa...

Semidefinite programming has been an interesting and active area of research for several years. In semidefinite programming one optimizes a convex (often linear) objective function subject to a system of linear matrix inequality constraints. Despite its numerous applications, algorithms for solving semidefinite programming problems are restricted to problems of moderate size because the computa...