Efficient Linear Search Algorithms for the Logarithmic Barrier Function

Abstract

Linear search algorithms are developed for use when minimizing logarithmic barrier functions, whose one-dimensionalbehavior is in general modeled poorly by the low-order polynomial approximations of standard linear search procedures. The new methods are based on special approximating functions with a logarithmic singularity, and are designed to utilize the same information as procedures based on special approximating functions with a logarithmic singularity, and are designed to utilize the same information as procedures based on quadratic or cubic polynomials. Although the parameters of the special approximating functions depend nonlinearly on the available data, the determination of the parameters requires little additional work in comparison with polynomial fits. Use of the special approximating functions has led to a significant improvement in efficiency when minimizing logarithmic barrier functions, where efficiency is measured by the number of function (or function and gradient) evaluations required for termination of each linear search.

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1976
Accession Number
ADA033432

Entities

People

  • Margaret H. Wright
  • Walter Murray

Organizations

  • Stanford University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Accuracy
  • Algorithms
  • Coefficients
  • Computers
  • Convergence
  • Efficiency
  • Equations
  • Extrapolation
  • Interpolation
  • Iterations
  • New York
  • Numerical Analysis
  • Polynomials
  • Square Roots
  • Test And Evaluation
  • United States
  • United States Government

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Systems Analysis and Design

Technology Areas

  • AI & ML
  • AI & ML - Bayesian Inference
  • AI & ML - Machine Learning Algorithms