Conic Methods for Unconstrained Minimization and Tensor Methods for Nonlinear Equations

Abstract

Standard methods for nonlinear equations and unconstrained minimization base each iteration on a linear or quadratic model of the objective function respectively. Recently, methods using two generalizations of the standard models have been proposed for these problems. Conic methods for unconstrained minimization use a model that is the ratio of a quadratic function divided by the square of a linear function. Tensor methods for nonlinear equations augment the standard linear model with a simple second order term. This paper surveys the research to date on methods. for unconstrained minimization and nonlinear equations that use conic and tensor models. It begins with a brief summary of the standard methods, so that the paper is essentially self-contained.

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1982
Accession Number
ADA606865

Entities

People

  • Robert B. Schnabel

Organizations

  • University of Colorado Boulder

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Algorithms
  • Arithmetic
  • Computational Science
  • Computer Programming
  • Computer Science
  • Computers
  • Convergence
  • Convex Sets
  • Equations
  • Interpolation
  • Iterations
  • Linear Systems
  • Mathematical Programming
  • New York
  • Numerical Analysis
  • Optimization
  • Standards

Fields of Study

  • Mathematics

Readers

  • Linear Algebra
  • Operations Research