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Journal of Optimization Theory and Applications

, Volume 47, Issue 1, pp 51–64 | Cite as

Numerical decomposition of a convex function

  • M. Lamoureux
  • H. Wolkowicz
Contributed Papers

Abstract

Given then×p orthogonal matrixA and the convex functionf:RnR, we find two orthogonal matricesP andQ such thatf is almost constant on the convex hull of ± the columns ofP, f is sufficiently nonconstant on the column space ofQ, and the column spaces ofP andQ provide an orthogonal direct sum decomposition of the column space ofA. This provides a numerically stable algorithm for calculating the cone of directions of constancy, at a pointx, of a convex function. Applications to convex programming are discussed.

Key Words

Convex functions convex programming cone of directions of constancy numerical stability 

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Copyright information

© Plenum Publishing Corporation 1985

Authors and Affiliations

  • M. Lamoureux
    • 1
  • H. Wolkowicz
    • 2
  1. 1.Department of MathematicsUniversity of California at BerkeleyBerkeley
  2. 2.Department of MathematicsUniversity of AlbertaEdmontonCanada

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