Computing a trust region step

Journal Article · Thu Sep 01 04:00:00 EDT 1983 · SIAM J. Sci. Stat. Comput.; (United States)

DOI:https://doi.org/10.1137/0904038· OSTI ID:5882782

More, J J; Sorensen, D C

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-31109-ENG-38
• OSTI ID: 5882782
• Journal Information: SIAM J. Sci. Stat. Comput.; (United States), Journal Name: SIAM J. Sci. Stat. Comput.; (United States) Vol. 4:3; ISSN SIJCD
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990200* -- Mathematics & Computers
ALGORITHMS
COMPUTER CALCULATIONS
COMPUTER CODES
G CODES
ITERATIVE METHODS
MATHEMATICAL LOGIC
NEWTON METHOD
OPTIMIZATION