Showing papers by "John E. Dennis published in 1985"

Optimization on Microcomputers: The Nelder-Mead Simplex Algorithm

Abstract: : In this paper we describe the Nelder-Mead simplex method for obtaining the minimizer of a function. The Nelder-Mead algorithm has several properties that make it a natural choice for implementation and utilization on microcomputers. Stopping criteria for the method are presented as well as a brief discussion of the convergence properties of the method. An algorithmic statement of the method is included as an appendix.

Least-Change Sparse Secant Update Methods with Inaccurate Secant Conditions

Abstract: We investigate the role of the secant or quasi-Newton condition in the sparse Broyden or Schubert update method for solving systems of nonlinear equations whose Jacobians are either sparse, or can be approximated acceptably by conveniently sparse matrices. We develop a theory on perturbations to the secant equation that will still allow a proof of local q-linear convergence. To illustrate the theory, we show how to generalize the standard secant condition to the case when the function difference is contaminated by noise.

A Memoryless Augmented Gauss-Newton Method for Nonlinear Least-Squares Problems

Abstract: : In this paper, we develop, analyze, and test a new algorithm for nonlinear least-squares problems. The algorithm uses a BFGS update of the Gauss-Newton Hessian when some hueristics indicate that the Gauss-Newton method may not make a good step. Some important elements are that the secant or quasi-Newton equations considered are not the obvious ones, and the method does not build up a Hessian approximation over several steps. The algorithm can be implemented easily as a modification of any Gauss-Newton code, and it seems to be useful for large residual problems.