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Mathematical Programming

, Volume 112, Issue 2, pp 403–425 | Cite as

Dual multilevel optimization

  • Timothy A. Davis
  • William W. HagerEmail author
Full Length Paper

Abstract

We study the structure of dual optimization problems associated with linear constraints, bounds on the variables, and separable cost. We show how the separability of the dual cost function is related to the sparsity structure of the linear equations. As a result, techniques for ordering sparse matrices based on nested dissection or graph partitioning can be used to decompose a dual optimization problem into independent subproblems that could be solved in parallel. The performance of a multilevel implementation of the Dual Active Set algorithm is compared with CPLEX Simplex and Barrier codes using Netlib linear programming test problems.

Keywords

Multilevel optimization Dual optimization Dual separability Dual active set algorithm Parallel algorithms 

Mathematics Subject Classification (2000)

90C05 90C06 65Y20 

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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Department of Computer and Information Science and EngineeringUniversity of FloridaGainesvilleUSA
  2. 2.Department of MathematicsUniversity of FloridaGainesvilleUSA

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