A quartic nonlinear optimization method

Authors:
N. Prabhu;W. He
Affiliations:
School of Industrial Engineering, Purdue University, West Lafayette, IN;School of Industrial Engineering, Purdue University, West Lafayette, IN
Venue:
Neural, Parallel & Scientific Computations
Year:
2002

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Abstract

In this paper we present a new algorithm - called the quartic method - for one-dimensional optimization. The quartic method is the third and final member of a family of algorithms called the Taylor Approximation Methods which includes Newton's method and Euler's method. Like its two distinguished relatives, the new method is also expected to be very efficient in practice. We present preliminary numerical results comparing the quartic method with both Newton's method and other fourth order algorithms. The numerical results suggest that the new method is significantly faster than Newton's method (and other fourth order algorithms) both in terms of the number of iterations and the actual running time. Theoretical considerations and preliminary numerical results suggest that the quartic method could emerge as a serious candidate for practical use in the future.