Abstract
A primal–dual decomposition method is presented to solve the separable convex programming problem. Convergence to a solution and Lagrange multiplier vector occurs from an arbitrary starting point. The method is equivalent to the proximal point algorithm applied to a certain maximal monotone multifunction. In the nonseparable case, it specializes to a known method, the proximal method of multipliers. Conditions are provided which guarantee linear convergence.
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This research was sponsored, in part, by the Air Force Office of Scientific Research under grant 80-0195.
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Spingarn, J.E. Applications of the method of partial inverses to convex programming: Decomposition. Mathematical Programming 32, 199–223 (1985). https://doi.org/10.1007/BF01586091
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DOI: https://doi.org/10.1007/BF01586091