6 research outputs found
Local properties and augmented Lagrangians in fully nonconvex composite optimization
A broad class of optimization problems can be cast in composite form, that
is, considering the minimization of the composition of a lower semicontinuous
function with a differentiable mapping. This paper discusses the versatile
template of composite optimization without any convexity assumptions. First-
and second-order optimality conditions are discussed, advancing the variational
analysis of compositions. We highlight the difficulties that stem from the lack
of convexity when dealing with necessary conditions in a Lagrangian framework
and when considering error bounds. Building upon these characterizations, a
local convergence analysis is delineated for a recently developed augmented
Lagrangian method, deriving rates of convergence in the fully nonconvex
setting.Comment: 42 page