A Family of Trust Region Based Algorithms for Unconstrained Minimization with Strong Global Convergence Properties.
Abstract
This paper has two aims: to exhibit very general conditions under which members of a broad class of unconstrained minimization algorithms are globally convergent in a strong sense, and to propose several new algorithms that use second derivative information and achieve such convergence. In the first part of the paper, we present a general trust region based algorithm schema that includes an undefinded step selection strategy. We give general conditions on this step selection strategy under which limit points of the algorithm will satisfy first and second order necessary conditions for unconstrained minimization. Our algorithm schema is sufficiently broad to include line search algorithms as well. Next, we show that a wide range of step selection strategies satisfy the requirements of our convergence theory. This leads us to propose several new algorithms that use second derivative information and achieve strong global convergence, including an indefinite line search algorithm, several indefinite dogleg algorithms, and a modified optimal-step algorithm. Finally, we propose an implementation of one such indefinite dogleg algorithm. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 10, 1982
- Accession Number
- ADA115785
Entities
People
- Gerald A. Shultz
- Richard H. Byrd
- Robert B. Schnabel
Organizations
- University of Colorado Boulder