Spline and Weighted Random Directions Method for Nonlinear Optimization.
Abstract
This article considers the problem of determining the optimal value and corresponding optimal point of a real function F in M variables. Only function values are given and the computation of derivatives is either not practical or are not available. Bremermann introduced an ingeneous and useful optimization algorithm that is guaranteed to converge for polynomials in several variables up to fourth degree. The heart of this method is the use of random directions of search together with a Lagrangian interpolation scheme. This author, having had extensive experience with this algorithm, found that the method has fast convergence at the early stages and tends to stagnate in the neighborhood of the optimal point. Motivated by the usefulness of random directions it is the purpose of this article to present an algorithm based on the proper use of interpolation schemes; (a) Lagrangian interpolations (such as those in Bremermann's methods); (b) spline approximations with variable nodes; (c) pseudo Newton steps using the spline derivatives (not the function); together with a search procedure along weighted random directions. The directions are chosen to be orthogonal using the Gram Schmidt orthogonalization procedure. This algorithm was extensively used for problem solving in mathematical biology, chemical kinetics, and general dynamical systems.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1984
- Accession Number
- ADA144217
Entities
People
- J. Milstein
Organizations
- University of California, Los Angeles