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A multi-start global minimization algorithm with dynamic search trajectories. (English) Zbl 0595.90073
A new multi-start algorithm for global unconstrained minimization is presented in which the search trajectories are derived from the equation of motion of a particle in a conservative force field, where the function to be minimized represents the potential energy. The trajectories are modified to increase the probability of convergence to a comparatively low local minimum, thus increasing the region of convergence of the global minimum. A Bayesian argument is adopted by which, under mild assumptions, the confidence level that the global minimum has been attained may be computed. When applied to standard and other test functions, the algorithm never failed to yield the global minimum.

MSC:
90C30 Nonlinear programming
49M37 Numerical methods based on nonlinear programming
65K05 Numerical mathematical programming methods
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