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Trajectory nets connecting all critical points of a smooth function

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Abstract

The disconnected components of certain trajectory nets containing all critical points of a differentiable functionf can be connected by suitably chosen contour sets of a certain associated functiong. A recursive construction yields a locally 1-dimensional connected set Ω which contains all critical points. The possible ways of tracing this set numerically are discussed.

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References

  1. F.H. Branin, Jr., “A widely convergent method for finding multiple solutions of simultaneous nonlinear equations,”IBM Journal of Research and Development 16 (1972) 504–522.

    Article  MATH  MathSciNet  Google Scholar 

  2. I. Diener, “On nonuniqueness in nonlinearL 2-approximation”,Journal of Approximation Theory (to appear).

  3. I. Diener, “On the global convergence of path-following methods to determine all solutions to a system of nonlinear equation,”NAM-Bericht 48 (1985).

  4. H.Th. Jongen, P. Jonker and F. Twilt, “On Newton flows in optimisation,”Methods of Operations Research 31 (1979) 345–359.

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This work was supported by the Deutsche Forschungsgemeinschaft.

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Diener, I. Trajectory nets connecting all critical points of a smooth function. Mathematical Programming 36, 340–352 (1986). https://doi.org/10.1007/BF02592065

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  • DOI: https://doi.org/10.1007/BF02592065

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