# Applications of the method of partial inverses to convex programming: Decomposition

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DOI: 10.1007/BF01586091

- Cite this article as:
- Spingarn, J.E. Mathematical Programming (1985) 32: 199. doi:10.1007/BF01586091

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## 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.

### Key words

Monotone Multifunction Separable Convex Programming Proximal Point Algorithm Decomposition Algorithm Resource Allocation Large-Scale Programming## Copyright information

© The Mathematical Programming Society, Inc. 1985