Nonsmooth optimization methods for parallel decomposition of multicommodity flow problems |
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Authors: | Renato De Leone Manlio Gaudioso Maria Flavia Monaco |
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Affiliation: | (1) Center for Parallel Optimization, Computer Sciences Department, University of Wisconsin-Madison, 1210 West Dayton Street, 53706 Madison, WI, USA;(2) Dipartimento di Elettronica, Informatica e Sistemistica, Università della Calabria, 87030 Rende, Cosenza, Italy |
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Abstract: | We develop an iterative algorithm based on right-hand side decomposition for the solution of multicommodity network flow problems. At each step of the proposed iterative procedure the coupling constraints are eliminated by subdividing the shared capacity resource among the different commodities and a master problem is constructed which attempts to improve sharing of the resources at each iteration.As the objective function of the master problem is nonsmooth, we apply to it a new optimization technique which does not require the exact solutions of the single commodity flow subproblems. This technique is based on the notion of - subgradients instead of subgradients and is suitable for parallel implementation. Extensions to the nonlinear, convex separable case are also discussed.The work of this author has been supported by the Air Force Office of Scientific Research Grant AFOSR-89-0410. |
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Keywords: | Nonsmooth optimization parallel decomposition multicommodity network flow problems |
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