Session: Variational Analysis: Theory and Applications IV
Chair: Walaa Moursi
Cluster: Nonsmooth Optimization
Talk 1: ADMM-Like Approximate Augmented Lagrangian Methods
Speaker: Jonathan Eckstein
Abstract: This talk discusses augmented Lagrangian methods for minimizing the sum of two convex functions, one smooth and one prox-friendly. By using duality manipulations or exploiting the smoothness of Moreau envelopes, the inner loops of these methods can be made to resemble the ADMM, but in a form in which acceleration techniques for forward and forward-backward first-order methods can be applied in a "plug-and-play" manner. The talk will also discuss new kinds of approximate augmented Lagrangian methods in which over- or under-relaxation of the multiplier update is adjusted to match the accuracy of the subproblem solution. This work is co-authored with Chang Yu, a graduate student at Rutgers University.
Talk 2: TBA
Speaker: Walaa Moursi
Abstract: TBA
Talk 3: Eckstein-Ferris-Pennanen-Robinson duality revisited: paramonotonicity, total Fenchel-Rockallar duality, and the Chambolle-Pock operator
Speaker: Shambhavi Singh
Abstract: Finding zeros of the sum of two maximally monotone operators involving a continuous linear operator is a central problem in optimization and monotone operator theory. We revisit the duality framework proposed by Eckstein, Ferris, Pennanen, and Robinson from a quarter of a century ago. Paramonotonicity is identified as a broad condition ensuring that saddle points coincide with the closed convex rectangle formed by the primal and dual solutions. Additionally, we characterize total duality in the subdifferential setting and derive projection formulas for sets that arise in the analysis of the Chambolle-Pock algorithm within the recent framework developed by Bredies, Chenchene, Lorenz, and Naldi.
