5 research outputs found
Momentum-inspired Low-Rank Coordinate Descent for Diagonally Constrained SDPs
We present a novel, practical, and provable approach for solving diagonally
constrained semi-definite programming (SDP) problems at scale using accelerated
non-convex programming. Our algorithm non-trivially combines acceleration
motions from convex optimization with coordinate power iteration and matrix
factorization techniques. The algorithm is extremely simple to implement, and
adds only a single extra hyperparameter -- momentum. We prove that our method
admits local linear convergence in the neighborhood of the optimum and always
converges to a first-order critical point. Experimentally, we showcase the
merits of our method on three major application domains: MaxCut, MaxSAT, and
MIMO signal detection. In all cases, our methodology provides significant
speedups over non-convex and convex SDP solvers -- 5X faster than
state-of-the-art non-convex solvers, and 9 to 10^3 X faster than convex SDP
solvers -- with comparable or improved solution quality.Comment: 10 pages, 8 figures, preprint under revie