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Computing a Trust Region Step

Description: An algorithm is proposed for the problem of minimizing a quadratic function subject to an ellipsoidal constraint which is guaranteed to produce a nearly optimal solution in a finite number of iterations. A robust and efficient algorithm for this problem is required to compute the step between iterates in trust region methods for optimization problems. We also consider the use of our algorithm in a trust region Newton's method. In particular, we prove that under reasonable assumptions the sequen… more
Date: December 1981
Creator: Moré, Jorge J. & Sorensen, D. C.
Partner: UNT Libraries Government Documents Department
open access

Newton's Method

Description: Newton's method plays a central role in the development of numerical techniques for optimization. In fact, most of the current practical methods for optimization can be viewed as variations on Newton's method. It is therefore important to understand Newton's method as an algorithm in its own right and as a key introduction to the most recent ideas in this area. One of the aims of this expository paper is to present and analyze two main approaches to Newton's method for unconstrained minimizatio… more
Date: February 1982
Creator: Moré, Jorge J. & Sorensen, D. C.
Partner: UNT Libraries Government Documents Department
open access

Software for Estimating Sparse Jacobian Matrices

Description: In many nonlinear problems it is necessary to estimate the Jacobian matrix of a nonlinear mapping F. In large scale problems the Jacobian of F is usually sparse, and then estimation by differences is attractive because the number of differences can be small compared to the dimension of the problem. For example, if the Jacobian matrix is banded then the number of differences needed to estimate the Jacobian matrix is, at most, the width of the band. In this paper we describe a set of subroutines … more
Date: July 1982
Creator: Coleman, Thomas F. & Moré, Jorge J.
Partner: UNT Libraries Government Documents Department
open access

User Guide for Minpack-1

Description: MINPACK-1 is a pack of FORTRAN subprograms for the numerical solution of nonlinear equations and nonlinear least-squares problems. This report provides an overview of the algorithms and software in the package, and includes the documentation and program listings.
Date: August 1980
Creator: Moré, Jorge J.; Garbow, Burton S. & Hillstrom, Kenneth E.
Partner: UNT Libraries Government Documents Department
open access

Implementation Guide for MINPACK-1

Description: MINPACK-1 is a package of Fortran subprograms for the numerical solution of systems of nonlinear equations and nonlinear least-squares problems. This report describes how to implement the package from the tape on which it is transmitted.
Date: July 1980
Creator: Garbow, B. S.; Hillstrom, Kenneth E. & Moré, Jorge J.
Partner: UNT Libraries Government Documents Department
open access

Estimation of Sparse Jacobian Matrices and Graph Coloring Problems

Description: Given a mapping with a sparse Jacobian matrix, the problem of minimizing the number of function evaluations needed to estimate the Jacobian matrix by differences is investigated. This problem can be attacked as a graph coloring problem and this approach leads to very efficient algorithms. The behavior of these algorithms is studied and, in particular, it is proved that two of the algorithms are optimal for band graphs. Numerical evidence is presented which indicates that these two algorithms ar… more
Date: June 1981
Creator: Coleman, Thomas F. & Moré, Jorge J.
Partner: UNT Libraries Government Documents Department
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