A Family of Variable-Metric Methods Derived by Variational Means

@inproceedings{Goldfarb2010AFO,
  title={A Family of Variable-Metric Methods Derived by Variational Means},
  author={Donald Goldfarb},
  year={2010}
}
A new rank-two variable-metric method is derived using Greenstadt's variational approach [Math. Comp., this issue]. Like the Davidon-Fletcher-Powell (DFP) variable-metric method, the new method preserves the positive-definiteness of the approximating matrix. Together with Greenstadt's method, the new method gives rise to a one-parameter family of variable-metric methods that includes the DFP and rank-one methods as special cases. It is equivalent to Broyden's one-parameter family [Math. Comp… CONTINUE READING
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References

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Showing 1-7 of 7 references

Broyden, "Quasi-Newton methods and their application to function minimisation,

  • C G.
  • Math. Comp., v
  • 1967
Highly Influential
10 Excerpts

Variations on variable metric methods,

  • J. Greenstadt
  • Math. Comp., v
  • 1970
3 Excerpts

Davidon, "Variance algorithm for minimization,

  • W C.
  • Comput. J., v
  • 1968
3 Excerpts

Sufficient conditions for the convergence of a variable metric algorithm,

  • D. Goldfarb
  • Proc. Confer, on Optimization (University of…
  • 1968
1 Excerpt

Another Variable Metric Method

  • P. Wolfe
  • Working Paper,
  • 1967
2 Excerpts

Davidon, Variable Metric Method for Minimization, A

  • W C.
  • E. C. Res. and Develop. Report ANL-5990 (Rev. TID…
  • 1959
1 Excerpt

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