A Software Package for Unconstrained Optimization Using Tensor Methods
Abstract
This paper describes a software package for finding the unconstrained minimizer of a nonlinear function of n variables. The package is intended for problems where n is not too large, say n < 100, so that the cost of storing one n x n matrix, and factoring it at each iteration, is acceptable. The software allows the user to choose between a recently developed tensor method for unconstrained optimization, and an analogous standard method based upon a quadratic model. The tensor method bases each iteration upon a specially constructed fourth order model of the objective function that is not significantly more expensive to form, store, or solve than the standard quadratic model. In our experience, the tensor method requires significantly fewer iterations and function evaluations to solve most unconstrained optimization problems than standard methods based upon quadratic models, and also solves a somewhat wider range of problems. For these reasons, it may be a useful addition to numerical software libraries.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 31, 1990
- Accession Number
- ADA233989
Entities
People
- Elizabeth Eskow
- Robert B. Schnabel
- Ta-tung Chow
Organizations
- University of Colorado Boulder