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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1976
- Accession Number
- ADA033432
Entities
People
- Margaret H. Wright
- Walter Murray
Organizations
- Stanford University