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.

翻译：我们提出了一个新颖的、实用的和可验证的方法,用加速的非convex编程来解决在规模上受非convex限制的半确定性编程问题。我们的算法非三边结合了从convex优化加速动作与协调电流转换和矩阵因子化技术。算法非常简单,可以执行,只增加一个单倍超参数 -- -- 动力。我们证明我们的方法在最佳的邻里承认局部线性趋同,并且总是与第一阶临界点汇合。我们实验性地在三个主要应用领域展示我们的方法的优点:MaxCut、MaxSAT和MIMO信号探测。在所有情况下,我们的方法都为非convex和convex SDP解答器提供显著的加速,速度比最先进的非convex解答器快5X,比SDP解答器快9至10°3X,比Convex SDP解答器快9至10°3 X -- -- 其溶质可比较或改进。