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  • nonlinear equations  (1)
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    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 97 (1998), S. 211-227 
    ISSN: 1573-2878
    Keywords: Homotopy ; relaxation ; trajectory tracking ; global optimization ; roots ; nonlinear equations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
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