Description: Based on the classic augmented Lagrangian multiplier method, we propose, analyze and test an algorithm for solving a class of equality-constrained nonsmooth optimization problems (chiefly but not necessarily convex programs) with
a particular structure. The algorithm effectively combines an alternating direction
technique with a nonmonotone line search to minimize the augmented Lagrangian
function at each iteration. We establish convergence for this algorithm, and apply it
to solving problems in image reconstruction with total variation regularization.
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