An Algorithm for Minimizing a Differentiable Function Subject to Box Constraints and Errors.
Abstract
Consider the problem of minimizing a differentiable function of n parameters with the parameters restricted to a box in n-space. A variable metric algorithm designed for this problem is described. It uses the symmetric rank one update formula, so that no matrix projections at the boundary of the box are necessary; and consequently, a Hessian approximation on the subspace spanned by the directions previously searched is available at each iteration to use in determining which constraints to drop. Moreover, the algorithm is designed to handle problems where the function and its gradient are evaluated with error. The difficulties associated with the symmetric rank one update formula and used to argue against its implementation have seldom been encountered in numerical experience to date and are circumvented. Numerical examples are presented which show (1) The algorithm presented compares favorably with Fletcher's excellent unconstrained minimization program available from Harwell and (2) On box-constrained problems, the algorithm is reliable and efficient. Problems with and without errors in the function and gradient values were considered.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 10, 1977
- Accession Number
- ADA042916
Entities
People
- Jane Cullum
- R. K. Brayton
Organizations
- IBM Thomas J. Watson Research Center