A Family of Trust Region Based Algorithms for Unconstrained Minimization with Strong Global Convergence Properties.

@article{Shultz1982AFO,
  title={A Family of Trust Region Based Algorithms for Unconstrained Minimization with Strong Global Convergence Properties.},
  author={Gerald A. Shultz and Robert B. Schnabel and Richard H. Byrd},
  journal={SIAM Journal on Numerical Analysis},
  year={1982},
  volume={22},
  pages={47-67}
}
This paper has two aims: to exhibit very general conditions under which members of a broad class of unconstrained minimization algorithms are globally convergent in a strong sense, and to propose several new algorithms that use second derivative information and achieve such convergence. In the first part of the paper we present a general trust-region-based algorithm schema that includes an undefined step selection strategy. We give general conditions on this step selection strategy under which… 
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References

A Family of Trust Region Based Algorithms for Unconstrained Minimization with Strong Global Convergence Properties ; CU-CS-216-82
  • Computer Science Technical Reports. Paper
  • 1982