A Curvilinear Search Using Tridiagonal Secant Updates for Unconstrained Optimization

Abstract

The idea of doing a curvilinear search along the Levenberg-Marquardt path s(mu) = -g/(H + muI) always has been appealing, but the cost of solving a linear system for each trial value of the parameter mu has discouraged its implementation. In this paper, an algorithm for searching along a path which includes s(mu) is studied. The algorithm uses a special inexpensive QTcQ-superscript-T to QT+Q-superscript-T Hessian update which trivializes the linear algebra required to compute s(mu). This update is based on earlier work of Dennis-Marwil and Martinez on least-change secant updates of matrix factors. The new algorithm is shown to be local and q-superlinearily convergent to stationary points, and to be globally q-superlinearily convergent for quasi-convex functions. Computational tests are given that show the new algorithm to be robust and efficient.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1990
Accession Number
ADA455265

Entities

People

  • C. Vaccino
  • H. D. Scolnik
  • J. E. Dennis
  • J. M. Martinez
  • M. T. Guardarucci
  • N. Echebest

Organizations

  • Rice University

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Algebra
  • Algorithms
  • Applied Mathematics
  • Argentina
  • Heuristic Methods
  • Information Operations
  • Linear Algebra
  • Linear Systems
  • Mathematics
  • Operations Research
  • Optimization

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Operations Research