Traditional nonlinear optimization - both theory and computation - relies heavily on the "active set" of constraints. Those constraints typically define a smooth surface, a crucial tool for analysis and algorithm design. This talk takes a less classical look at the geometry of this surface, using variational and semi-algebraic analysis. A proximal algorithm for composite optimization illustrates the potential.
Joint work with J. Bolte, A. Daniilidis, D. Drusvyatskiy, and S. Wright.