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.

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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

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Computer Programming
  • Computer Science
  • Computers
  • Four Dimensional
  • Iterations
  • Military Research
  • Numbers
  • Optimization
  • Precision
  • Procedures (Computers)
  • Real Numbers
  • Real Variables
  • Standards
  • Test And Evaluation
  • Test Sets
  • User Interface

Readers

  • Computational Modeling and Simulation
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Linear Algebra