Note on a paper of Broyden

  • Authors:

  • Cornelis Roos;TamáS Terlaky

  • Affiliations:

  • Faculty of Information Technology and Systems, Department TWI/SSOR, Delft University of Technology, P.O. Box 5031, 2600 GA Delft, The Netherlands;Faculty of Information Technology and Systems, Department TWI/SSOR, Delft University of Technology, P.O. Box 5031, 2600 GA Delft, The Netherlands

  • Venue:
  • Operations Research Letters
  • Year:
  • 1999

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Abstract

Recently, Broyden [Optim. Methods Software 8 (3-4) (1998) 185-199] proved a property of orthogonal matrices from which he derived Farkas' lemma and some related results. It is shown that Broyden's result straightforwardly follows from well-known theorems of the alternative, like Motzkin's transposition theorem and Tucker's theorem, which are all logically equivalent to Farkas' lemma; we also answer the question of Broyden on how to efficiently compute the sign matrix of an orthogonal matrix. Finally, we raise some related questions about possible generalizations of Broyden's result.