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. http://resolver.caltech.edu/CaltechAUTHORS:20120808-152034153
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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.
|Additional Information:||© 1998 Plenum Publishing Corporation Communicated by F. E. Udwadia|
|Subject Keywords:||Homotopy, relaxation, trajectory tracking, global optimization, roots, nonlinear equations.|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Sydney Garstang|
|Deposited On:||08 Aug 2012 23:04|
|Last Modified:||08 Aug 2012 23:04|
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