We introduce a first order method for solving very large convex cone
programs. The method uses an operator splitting method, the alternating
directions method of multipliers, to solve the homogeneous self-dual embedding,
an equivalent feasibility problem involving finding a nonzero point in the
intersection of a subspace and a cone. This approach has several favorable
properties. Compared to interior-point methods, first-order methods scale to
very large problems, at the cost of requiring more time to reach very high
accuracy. Compared to other first-order methods for cone programs, our approach
finds both primal and dual solutions when available or a certificate of
infeasibility or unboundedness otherwise, is parameter-free, and the
per-iteration cost of the method is the same as applying a splitting method to
the primal or dual alone. We discuss efficient implementation of the method in
detail, including direct and indirect methods for computing projection onto the
subspace, scaling the original problem data, and stopping criteria. We describe
an open-source implementation, which handles the usual (symmetric)
non-negative, second-order, and semidefinite cones as well as the
(non-self-dual) exponential and power cones and their duals. We report
numerical results that show speedups over interior-point cone solvers for large
problems, and scaling to very large general cone programs.

该研究提出了一种用于解决大规模凸锥问题的一阶方法，该方法使用交替方向乘子法来解决自对偶嵌入问题，该方法不需要参数，可以找到原始解和对偶解，并且在大规模优化问题上表现出色。