Computing a trust region step
An algorithm is proposed for the problem of minimizing a quadratic function subject to an ellipsoidal constraint and it is shown that this algorithm is guaranteed to produce a nearly optimal solution in a finite number of iterations. We also consider the use of this algorithm in a trust region Newton's method. In particular, we prove that under reasonable assumptions the sequence generated by Newton's method has a limit point which satisfies the first and second order necessary conditions for a minimizer of the objective function. Numerical results for GQTPAR, which is a Fortran implementation of our algorithm, show that GQTPAR is quite successful in a trust region method. In our tests a call to GQTPAR only required 1.6 iterations on the average.
- Research Organization:
- Argonne National Lab., IL
- DOE Contract Number:
- W-31-109-ENG-38
- OSTI ID:
- 5882782
- Journal Information:
- SIAM J. Sci. Stat. Comput.; (United States), Vol. 4:3
- Country of Publication:
- United States
- Language:
- English
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