The full approximation storage (FAS) scheme is a widely used multigrid method
for nonlinear problems. In this paper, a new framework to design and analyze
FAS-like schemes for convex optimization problems is developed. The new method,
the Fast Subspace Descent (FASD) scheme, which generalizes classical FAS, can
be recast as an inexact version of nonlinear multigrid methods based on space
decomposition and subspace correction. The local problem in each subspace can
be simplified to be linear and one gradient descent iteration (with an
appropriate step size) is enough to ensure a global linear (geometric)
convergence of FASD.Comment: 33 page
