Convergence rates with inexact non-expansive operators

摘要: In this paper, we present a convergence rate analysis for the inexact Krasnosel'skiăź---Mann iteration built from non-expansive operators. The presented results include two main parts: first establish global pointwise and ergodic iteration-complexity bounds; then, under metric sub-regularity assumption, local linear distance of iterates to set fixed points. obtained can be applied analyze various monotone operator splitting methods in literature, including Forward---Backward splitting, Generalized Forward---Backward, Douglas---Rachford alternating direction method multipliers Primal---Dual methods. For these methods, also develop easily verifiable termination criteria finding an approximate solution, which seen as generalization criterion classical gradient descent method. We finally parallel non-stationary iteration.