Generalized Trajectory Methods for Finding Multiple Extrema and Roots of Functions

C. M. Yang and J. L. Beck
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C. M. Yang: California Institute of Technology
J. L. Beck: California Institute of Technology

Journal of Optimization Theory and Applications, 1998, vol. 97, issue 1, No 11, 227 pages

Abstract: 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 connects other stationary points in the specified region by a network of trjectories. 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.

Keywords: Homotopy; relaxation; trajectory tracking; global optimization; roots; nonlinear equations (search for similar items in EconPapers)
Date: 1998
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DOI: 10.1023/A:1022635419332

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