Accession Number : ADA057962
Title : Numerical Algorithms for Nonlinearly Constrained Optimization.
Descriptive Note : Doctoral thesis,
Corporate Author : STANFORD UNIV CALIF DEPT OF COMPUTER SCIENCE
Personal Author(s) : Heath,Michael Thomas
Report Date : APR 1978
Pagination or Media Count : 150
Abstract : This dissertation is concerned with the development and numerical implementation of algorithms for solving finite dimensional optimization problems. Special emphasis is given to robustness, by which is meant the ability of an algorithm to cope with adverse circumstances, whether due to pathologies of a particular problem or to the shortcomings of finite precision computer arithmetic. A uniform framework is developed in which a common set of techniques may be applied to all of the standard problems of optimization. The algorithms are based on Newton-like methods implemented in a robust manner by means of hybrid, curved line searches and stable linear algebra techniques. Developed first in the context of systems of nonlinear equations, nonlinear least squares, and unconstrained minimization, the algorithms are combined and extended to include problems with equality or inequality constraints. Constrained problems are handled by means of separate line searches in the range and null spaces of the matrix of constraint normals. The classical Lagrangian is modified to allow the same Newton-like methods to be applied to inequality constraints. Test results are presented which show the validity and promise of the methods developed in this dissertation. (Author)
Descriptors : *ALGORITHMS, *NUMERICAL ANALYSIS, OPTIMIZATION, COMPUTER PROGRAMMING, THESES, PROBLEM SOLVING, THEOREMS.
Subject Categories : Theoretical Mathematics
Computer Programming and Software
Distribution Statement : APPROVED FOR PUBLIC RELEASE