Augmented Lagrangians and Applications of the Proximal Point Algorithm in Convex Programming
R. TYRRELL ROCKAFELLAR · Mathematics of Operations Research · 1976
The theory of the proximal point algorithm for maximal monotone operators is applied to three algorithms for solving convex programs, one of which has not previously been formulated. Rate-of-convergence results for the “method of multipliers,” of the strong sort already known, are derived in a generalized form relevant also to problems beyond the compass of the standard second-order conditions for oplimality. The new algorithm, the “proximal method of multipliers,” is shown to have much the same convergence properties, but with some potential advantages.