Active‐Set Newton Methods and Partial Smoothness

Diverse optimization algorithms correctly identify, in finite time, intrinsic constraints that must be active at optimality. Analogous behavior extends beyond to systems involving partly smooth operators, and particular variational inequalities over sets. As classical nonlinear programming, such active‐set structure underlies the design of accelerated local Newton type. We formalize this idea broad generality as a simple linearization scheme for two intersecting manifolds.