Session: Variational Analysis: Theory and Applications III
Chair: Walaa Moursi
Cluster: Nonsmooth Optimization
Talk 1: Convex antiderivatives in multi-marginal settings
Speaker: Sedi Bartz
Abstract: We consider aspects of the convex analytic structure at the foundations of multi-marginal optimal transport. We present extensions of classical convex analysis and monotone operator theory, recent progress and open questions.
Talk 2: An invariance theory for complete characterization of exact optimal fixed-point algorithm family
Speaker: Taeho Yoon
Abstract: For nonexpansive fixed-point problems, both Halpern's method with optimal parameters and its so-called H-dual algorithm exhibit the exact optimal worst-case convergence rates. In this work, we completely characterize the infinite family of distinct algorithms using predetermined step-sizes, represented as lower triangular H-matrices, all of which attain the same optimal convergence rates. The characterization is based on algebraic quantities that we call H-invariants, whose values stay constant over all optimal H-matrices. The theory of H-invariants offers a novel view of optimal acceleration in first-order optimization as an algebraic study of carefully selected invariants and structures induced by them.
Talk 3: Canceled
Speaker: Scott Lindstrom
Abstract: Canceled
