Paper Info
Title
Approximate solution of the trust region problem by minimization over two-dimensional subspaces.
Abstract
The trust region problem, minimization of a quadratic function subject to a spherical trust region constraint, occurs in many optimization algorithms. In a previous paper, the authors introduced an inexpensive approximate solution technique for this problem that involves the solution of a two-dimensional trust region problem. They showed that using this approximation in an unconstrained optimization algorithm leads to the same theoretical global and local convergence properties as are obtained using the exact solution to the trust region problem. This paper reports computational results showing that the two-dimensional minimization approach gives nearly optimal reductions in then-dimension quadratic model over a wide range of test cases. We also show that there is very little difference, in efficiency and reliability, between using the approximate or exact trust region step in solving standard test problems for unconstrained optimization. These results may encourage the application of similar approximate trust region techniques in other contexts.
Year
DOI
Venue
1988
10.1007/BF01580735
Math. Program.
Keywords
Field
DocType
approximate solution,unconstrained optimization,trust region problem,trust region,two-dimensional subspaces,local convergence,quadratic equations,algorithms,reduction,optimization,two dimensional,exact solution,reliability
Exact solutions in general relativity,Trust region,Mathematical optimization,Quadratic equation,Linear subspace,Minification,Quadratic function,Local convergence,Test case,Mathematics
Journal
Volume
Issue
ISSN
40
1-3
0025-5610
Citations 
PageRank 
References 
66
10.76
3
Authors
3
Name
Order
Citations
PageRank
Richard H. Byrd12234227.38
Robert B. Schnabel2565143.88
Gerald A. Shultz36610.76