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Generalized Trajectory Methods for Finding Multiple Extrema and Roots of Functions

Yang, C. M. and Beck, J. L. (1998) Generalized Trajectory Methods for Finding Multiple Extrema and Roots of Functions. Journal of Optimization Theory and Applications, 97 (1). pp. 211-227. ISSN 0022-3239. doi:10.1023/A:1022635419332.

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Two generalized trajectory methods are combined to provide a novel and powerful numerical procedure for systematically finding multiple local extrema of a multivariable objective function. This procedure can form part of a strategy for global optimization in which the greatest local maximum and least local minimum in the interior of a specified region are compared to the largest and smallest values of the objective function on the boundary of the region. The first trajectory method, a homotopy scheme, provides a globally convergent algorithm to find a stationary point of the objective function. The second trajectory method, a relaxation scheme, starts at one stationary point and systematically connected other stationary points in the specified region by a network of trajectories. It is noted that both generalized trajectory methods actually solve the stationarity conditions, and so they can also be used to find multiple roots of a set of nonlinear equations.

Item Type:Article
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Additional Information:© 1998 Plenum Publishing Corporation Communicated by F. E. Udwadia
Subject Keywords:Homotopy, relaxation, trajectory tracking, global optimization, roots, nonlinear equations.
Issue or Number:1
Record Number:CaltechAUTHORS:20120808-152034153
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Official Citation:Yang, C.M. & Beck, J.L. Journal of Optimization Theory and Applications (1998) 97: 211. doi:10.1023/A:1022635419332
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:33032
Deposited By: Sydney Garstang
Deposited On:08 Aug 2012 23:04
Last Modified:09 Nov 2021 21:31

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