41 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
Faster quantum and classical SDP approximations for quadratic binary optimization
We give a quantum speedup for solving the canonical semidefinite programming relaxation for binary quadratic optimization. The class of relaxations for combinatorial optimization has so far eluded quantum speedups. Our methods combine ideas from quantum Gibbs sampling and matrix exponent updates. A de-quantization of the algorithm also leads to a faster classical solver. For generic instances, our quantum solver gives a nearly quadratic speedup over state-of-the-art algorithms. We also provide an efficient randomized rounding procedure that converts approximately optimal SDP solutions into constant factor approximations of the original quadratic optimization problem