Terry Rockafellar, University of Washington

Abstract

Multiplier methods based on augmented Lagrangians are attractive in convex and nonconvex programming for their stabilizing and even convexifying properties.  They have widely been seen, however, as incompatible with taking advantage of block-separable structure.

In fact, when articulated in the right way, they can produce decompostition algorithms in which low-dimensional subproblems can be solved in parallel.  Convergence in the nonconvex case is, of course, just local, but is available under a broad analog of the strong second-order sufficient condition for local optimality that dominates much of computational methodology outside of convex optimization. This carries over also to extended nonlinear programing with its greater flexibility to handle composite terms.

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