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High order Halley type directions

Bilel Kchouk(Bilel.Kchouk***at***Usherbrooke.ca)
Jean-Pierre Dussault(Jean-Pierre.Dussault***at***Usherbrooke.ca)

Abstract: The 1669-1670 Newton-Raphson’s method, the 1694 Halley and the 1839 Chebyshev methods are well known algorithms used in non linear programming. By considering these three methods as displacement directions, we introduce in this paper new high order algorithms using these famous methods. We develop two families of such directions and study their convergence and their complexity. We show that these new methods are quite efficient in terms of convergence and costs. We finally introduce a global algorithm based on our analysis of high order methods.

Keywords: Newton's method, Halley family method, automatic differentiation

Category 1: Nonlinear Optimization

Category 2: Nonlinear Optimization (Unconstrained Optimization )

Citation: submitted to : International Journal of Pure and Applied Mathematics

Download: [Postscript]

Entry Submitted: 12/12/2011
Entry Accepted: 12/12/2011
Entry Last Modified: 12/12/2011

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