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Analysis of the alternating direction method of multipliers for nonconvex problems
This work investigates the theoretical performance of the
alternating-direction method of multipliers (ADMM) as it applies to nonconvex
optimization problems, and in particular, problems with nonconvex constraint
sets. The alternating direction method of multipliers is an optimization method
that has largely been analyzed for convex problems. The ultimate goal is to
assess what kind of theoretical convergence properties the method has in the
nonconvex case, and to this end, theoretical contributions are two-fold. First,
this work analyzes the method with local solution of the ADMM subproblems,
which contrasts with much analysis that requires global solutions of the
subproblems. Such a consideration is important to practical implementations.
Second, it is established that the method still satisfies a local convergence
result. The work concludes with some more detailed discussion of how the
analysis relates to previous work