A Semismooth Newton Method for Fast, Generic Convex Programming
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Proceedings of the 34th International Conference on Machine Learning, PMLR 70:7079, 2017.
Abstract
We introduce NewtonADMM, a method for fast conic optimization. The basic idea is to view the residuals of consecutive iterates generated by the alternating direction method of multipliers (ADMM) as a set of fixed point equations, and then use a nonsmooth Newton method to find a solution; we apply the basic idea to the Splitting Cone Solver (SCS), a stateoftheart method for solving generic conic optimization problems. We demonstrate theoretically, by extending the theory of semismooth operators, that NewtonADMM converges rapidly (i.e., quadratically) to a solution; empirically, NewtonADMM is significantly faster than SCS on a number of problems. The method also has essentially no tuning parameters, generates certificates of primal or dual infeasibility, when appropriate, and can be specialized to solve specific convex problems.
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