Generalized Trajectory Methods for Finding Multiple Extrema and Roots of Functions
- Creators
- Yang, C. M.
- Beck, J. L.
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.
Additional Information
© 1998 Plenum Publishing Corporation Communicated by F. E. UdwadiaAdditional details
- Eprint ID
- 33032
- DOI
- 10.1023/A:1022635419332
- Resolver ID
- CaltechAUTHORS:20120808-152034153
- Created
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2012-08-08Created from EPrint's datestamp field
- Updated
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2021-11-09Created from EPrint's last_modified field