Projected Newton methods for optimization problems with simple constraints

  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},
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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Publications referenced by this paper.
Showing 1-9 of 9 references

A Zomput 3 tiorial Stuzy of . Active Set Strategies in Nonlinear ? rogrammine with

G. P. McCormick
The Variable Reduction Method for Nonlinear Programming " , Management Science • 1975

Introduction to Linear and Soniinear Programming, Addison-Wesley, Reading, Mass

D. G. Lcenberger

Murrav reds.). Sumerical Methods for Constrained timization

P. E. Gill

!Second Derivative Methods", in Numerical Methods for Unconstrained Optimization

W. Murray

Computational Methods in Optimization: A Unified Approach

E. Polak

The Variable Reduction Method for Nonlinear Programming

G. P. McCormick
Management Science, • 1970

Extension of Davidon's Variable Sletric Algorithm to Maximization Under Linear Inequality and Equality Constraints

I. Soldfarb
J. of Applied \lath., • 1969

Convex Programming in Hilbert Space

A. A. Goldstein
Bull. her. Math. SOC., • 1964

The Gradient Projection ? lethod for Nonlinear Programming , Part I : Linear Constraints "

U. M. Garcia-Palomares, O. L. Mangasarian, J. B. Rosen
Sumerical Methods for Constrained timization • 1960

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