Projected Newton methods for optimization problems with simple constraints

@article{Bertsekas1981ProjectedNM,
  title={Projected Newton methods for optimization problems with simple constraints},
  author={Dimitri P. Bertsekas},
  journal={1981 20th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes},
  year={1981},
  pages={762-767}
}
We consider the problem min {f(x)|x ¿ 0} and algorithms of the form xk+1 = [xk - ¿k Dk¿f(xk)]+ where [¿]+ denotes projection on the positive orthant, ¿k is a stepsize chosen by an Armijolike rule, and Dk is a positive definite symmetric matrix which is partly diagonal. We show that Dk can be calculated simply on the basis of second derivatives of f so that the resulting Newton-like algorithm has a typically superlinear rate of convergence. With other choices of Dk convergence at a typically… CONTINUE READING
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