Relaxation Methods for Network Flow Problems with Convex Arc Costs | Zendy

Dimitri P. Bertsekas | Zendy; Patrick Hosein | Zendy; Paul Tseng | Zendy

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Relaxation Methods for Network Flow Problems with Convex Arc Costs

Author(s) -

Dimitri P. Bertsekas,

Patrick Hosein,

Paul Tseng

Publication year - 1987

Publication title -

siam journal on control and optimization

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.486

H-Index - 116

eISSN - 1095-7138

pISSN - 0363-0129

DOI - 10.1137/0325067

Subject(s) - mathematics , relaxation (psychology) , arc (geometry) , flow network , regular polygon , convergence (economics) , flow (mathematics) , gauss–seidel method , mathematical optimization , computation , dual (grammatical number) , iterative method , geometry , algorithm , psychology , social psychology , art , literature , economics , economic growth

We consider the standard single commodity network flow problem with both linear and strictly convex possibly nondifferentiable arc costs. For the case where all arc costs are strictly convex we study the convergence of a dual Gauss-Seide! type relaxation method that is well suited for parallel computation. We then extend this method to the case where some of the arc costs are linear. As a special case we recover a relaxation method for the linear minimum cost network flow problem proposed in Bertsekas (1) and Bertsekas and Tseng (2).

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