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.