Mathematical Programming

, Volume 94, Issue 1, pp 41–69

The volume algorithm revisited: relation with bundle methods

  • L. Bahiense
  • N. Maculan
  • C. Sagastizábal

Abstract.

 We revise the Volume Algorithm (VA) for linear programming and relate it to bundle methods. When first introduced, VA was presented as a subgradient-like method for solving the original problem in its dual form. In a way similar to the serious/null steps philosophy of bundle methods, VA produces green, yellow or red steps. In order to give convergence results, we introduce in VA a precise measure for the improvement needed to declare a green or serious step. This addition yields a revised formulation (RVA) that is halfway between VA and a specific bundle method, that we call BVA. We analyze the convergence properties of both RVA and BVA. Finally, we compare the performance of the modified algorithms versus VA on a set of Rectilinear Steiner problems of various sizes and increasing complexity, derived from real world VLSI design instances.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • L. Bahiense
    • 1
  • N. Maculan
    • 1
  • C. Sagastizábal
    • 2
  1. 1.Universidade Federal do Rio de Janeiro, COPPE-Sistemas e Computacão, P.O.Box 68511, Rio de Janeiro, RJ 21945-970, Brazil, e-mail: bahiense@impa.br, maculan@cos.ufrj.brBR
  2. 2.IMPA, Estrada Dona Castorina 110, Jardim Botânico, Rio de Janeiro RJ 22460-320, Brazil. On leave from INRIA- Rocquencourt, BP 105, 78153 Le Chesnay, FranceFR

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