Nonmonotone and Monotone Active-Set Methods for Image Restoration, Part 1: Convergence Analysis

Active-set methods based on augmented Lagrangian smoothing of nondifferentiable optimization problems arising in image restoration are discussed. One-dimensional image restoration problems and two different formulations of two-dimensional image restoration problems are given. Both nonmonotone and monotone active-set algorithms are described and finite-step convergence of the algorithms is considered.

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