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What kind of function can be minimized by going "downhill"

  1. Jan 28, 2015 #1
    Hi all:
    I'm looking for the name of a property that a function (of arbitrary dimension) has when you can continuously follow the steepest descent to get to the global minimum. Being "smooth" is necessary but not sufficient.

    For example, for just 1-D, this property is equivalent to being "convex", however the 2-D Rosenbrock function is a non-convex function, but still does have the property I'm looking for: any numerical algorithm will bring you quickly to the valley --it will then struggle to follow the valley to get to the global minimum, but at least in principle there is always a small-but-finite gradient that, if followed, will lead you to the global minimum which is the only stationary point. Therefore, the Rosenbrock function is a ..... function.

    Can anyone tell me what word I should use to finish that sentence?
  2. jcsd
  3. Jan 29, 2015 #2


    User Avatar

    Staff: Mentor

    I don't know a single word, but you can say that it is a function that has a global minimum but no local minima.
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