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. https://resolver.caltech.edu/CaltechAUTHORS:20120808-152034153
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Abstract
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 | ||||||||||||
DOI: | 10.1023/A:1022635419332 | ||||||||||||
Record Number: | CaltechAUTHORS:20120808-152034153 | ||||||||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20120808-152034153 | ||||||||||||
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 | ||||||||||||
Collection: | CaltechAUTHORS | ||||||||||||
Deposited By: | Sydney Garstang | ||||||||||||
Deposited On: | 08 Aug 2012 23:04 | ||||||||||||
Last Modified: | 09 Nov 2021 21:31 |
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