IJPAM: Volume 78, No. 6 (2012)

HIGH ORDER HALLEY TYPE DIRECTIONS

Bilel Kchouk$^1$, Jean-Pierre Dussault$^2$
$^{1,2}$Department of Mathematics
University of Sherbrooke
2500, Boul. de l'Université, Sherbrooke (Québec), J1K 2R1, CANADA


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.

Received: December 12, 2011

AMS Subject Classification: 49M15

Key Words and Phrases: Newton's method, Halley family method, automatic differentiation

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 78
Issue: 6