A Curvilinear Search Algorithm for Unconstrained Optimization by Automatic Differentiation
by
Domenico Conforti
D.E.I.S. University of Calabria 87030 Rende (CS) Italy
Coauthors: Marco Mancini (D.E.I.S. University of Calabria)

In this presentation we aim to propose a new approach for solving the unconstrained optimization problem minf(x), x in Reⁿ, based on the use of Automatic Differentiation techniques. We require that f:Reⁿ --> Re be continuously differentiable at least to the third order. In fact we developed a prototype algorithm which is based on local searches along a curvilinear trajectory in Reⁿ, computed by the explicit knowledge of the third order partial derivatives of the objective function at the current point. This strategy aims to overcome the typical behavior, in certain difficult situations, of a classical descent method which performs many short steps along linear monodimensional manifolds. The partial derivatives up to the third order were computed by using the AD software tool ADOL-C. Some preliminary numerical experiments were carried out with the aim to compare the prototype approach with well known Newton type algorithms. The results are quite encouraging especially in the case of very ill-conditioned problems.

http://www.parcolab.unical.it/~mancini/ad2000_opt.ps

Date received: December 29, 1999