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.
Similar content being viewed by others
References
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.
I. Diener, “On nonuniqueness in nonlinearL 2-approximation”,Journal of Approximation Theory (to appear).
I. Diener, “On the global convergence of path-following methods to determine all solutions to a system of nonlinear equation,”NAM-Bericht 48 (1985).
H.Th. Jongen, P. Jonker and F. Twilt, “On Newton flows in optimisation,”Methods of Operations Research 31 (1979) 345–359.
Author information
Authors and Affiliations
Additional information
This work was supported by the Deutsche Forschungsgemeinschaft.
Rights and permissions
About this article
Cite this article
Diener, I. Trajectory nets connecting all critical points of a smooth function. Mathematical Programming 36, 340–352 (1986). https://doi.org/10.1007/BF02592065
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02592065