Newton's method with a model trust-region modification
A modified Newton method for unconstrained minimization is presented and analyzed. The modification is based upon the model trust region approach. This report contains a thorough analysis of the locally constrained quadratic minimizations that arise as subproblems in the modified Newton iteration. Several promising alternatives are presented for solving these subproblems in ways that overcome certain theoretical difficulties exposed by this analysis. Very strong convergence results are presented concerning the minimization algorithm. In particular, the explicit use of second-order information is justified by demonstrating that the iterates converge to a point that satisfies the second-order necessary conditions for minimization. With the exception of very pathological cases this convergence occurs whenever the algorithm is applied to problems with continuous second partial derivatives.
- Research Organization:
- Argonne National Laboratory (ANL), Argonne, IL (United States)
- DOE Contract Number:
- W-31109-ENG-38
- OSTI ID:
- 6836252
- Report Number(s):
- ANL-80-106
- Country of Publication:
- United States
- Language:
- English
Similar Records
Trust-region methods for unconstrained minimization
A robust trust-region algorithm with a non-monotonic penality parameter scheme for constrained optimization