Unconstrained Minimization by Interpolation: Rates of Convergence.

Abstract

The main attraction of Newton's method for finding a stationary point is its quadratic convergence. However, it necessitates computation and inversion of the second order derivative matrix. Common minimization algorithms approximate the Hessian or its inverse by first order (i.e., gradient) information. First order information algorithms in common use are known to have at best superlinear rate of convergence. We analyze the rate of convergence of a new class of algorithms based on n-dimensional interpolation. In particular, we present a class of algorithms which use first order information only, while maintaining quadratic convergence.

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1980
Accession Number
ADA095025

Entities

People

  • J. Barzilai

Organizations

  • University of Texas at Austin

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Computations
  • Construction
  • Convergence
  • Equations
  • Interpolation
  • Intervals
  • Iterations
  • Numerical Analysis
  • Polynomials
  • Rational Functions
  • Sequences
  • Steepest Descent Method
  • Universities

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Operations Research
  • Theoretical Analysis.