Highly efficient Broyden methods of minimization with variable parameter

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Abstract

Recently. there has been an increasing interest in the self-scaling Broyden family of formulae. These formulae are usually defined by replacing the approximate Hessian matrix B by τ B for some scaling parameter τ. It is clear that if B is replaced by (l/τ)B in a self-scaling formula, then a member of the Broyden family follows. The author will show that tn certain cases this member is not uniquely defined. He will illustrate this point hy addressing new members of the Broyden family and giving a new approach to the self-dual update of Oren and Spedicato. The new members are defined by explicit expression, and satisfy the usual condition which ensures that the current Hessian approximations are maintained positive definite. Because comparison with the BFGS method shows promising numerical results, the corresponding new methods are efficient.

Original languageEnglish
Pages (from-to)301-310
Number of pages10
JournalOptimization Methods and Software
Volume1
Issue number4
DOIs
Publication statusPublished - 1992

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Keywords

  • Broyden's family
  • New members of the Broyden family
  • Quasi-Newton methods
  • Self-scaling formulae

ASJC Scopus subject areas

  • Control and Optimization
  • Software
  • Applied Mathematics

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