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A Semismooth Newton Method for Fast, Generic Convex Programming
Alnur Ali · Eric Wong · Zico Kolter

Tue Aug 08 01:30 AM -- 05:00 AM (PDT) @ Gallery #7

We introduce Newton-ADMM, 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 state-of-the-art method for solving generic conic optimization problems. We demonstrate theoretically, by extending the theory of semismooth operators, that Newton-ADMM converges rapidly (i.e., quadratically) to a solution; empirically, Newton-ADMM 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.

Author Information

Alnur Ali (Carnegie Mellon University)
Eric Wong (Carnegie Mellon University)
Zico Kolter (Carnegie Mellon University)

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