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We present a novel, practical, and provable approach for solving diagonallyconstrained semi-definite programming (SDP) problems at scale using acceleratednon-convex programming. Our algorithm non-trivially combines accelerationmotions from convex optimization with coordinate power iteration and matrixfactorization techniques. The algorithm is extremely simple to implement, andadds only a single extra hyperparameter -- momentum. We prove that our methodadmits local linear convergence in the neighborhood of the optimum and alwaysconverges to a first-order critical point. Experimentally, we showcase themerits of our method on three major application domains: MaxCut, MaxSAT, andMIMO signal detection. In all cases, our methodology provides significantspeedups over non-convex and convex SDP solvers -- 5X faster thanstate-of-the-art non-convex solvers, and 9 to 10^3 X faster than convex SDPsolvers -- with comparable or improved solution quality.

Momentum-inspired Low-Rank Coordinate Descent for Diagonally Constrained SDPs