Mathematical Programming

, Volume 32, Issue 2, pp 199-223

First online:

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

  • Jonathan E. SpingarnAffiliated withSchool of Mathematics, Georgia Institute of Technology

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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