Article ID: | iaor19951887 |
Country: | Netherlands |
Volume: | 62 |
Issue: | 2 |
Start Page Number: | 299 |
End Page Number: | 319 |
Publication Date: | Nov 1993 |
Journal: | Mathematical Programming |
Authors: | Mifflin Robert, Strodiot J.-J. |
This paper presents an algorithm for minimizing a function of one variable which uses function, but not derivative, values at five-points to generate each iterate. It employs quadratic and polyhedral approximations together with a safeguard. The basic method without the safeguard exhibits a type of better than linear convergence for certain piecewise twice continuously differentiable functions. The safeguard guarantees convergence to a stationary point for very general functions and preserves the better than linear convergence of the basic method.