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Topic: Step Control for Gradient Descent ?
Replies: 5   Last Post: Feb 23, 2009 1:46 PM

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Dave Rudolf

Posts: 37
Registered: 10/3/05
Re: Step Control for Gradient Descent ?
Posted: Feb 23, 2009 1:46 PM
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On Feb 18, 6:17 pm, Ray Vickson <> wrote:
> On Feb 18, 5:34 pm, wrote:

> > On Feb 18, 3:31 pm, wrote:
> > > Why am I making an issue of this? Well, there are two aspects to your
> > > problem: (1) getting a local optimum in reasonable time and with
> > > reasonable accuracy; and (2) getting a global optimum. Let's just look
> > > at (1) for the moment. It has long been known through examples that
> > > simple gradient searches (of the type you seem to be using) are
> > > dangerous: you can have convergence to a NON-OPTIMAL point.

> > What do you mean non-optimal? Of course it can converge on a local
> > minimum, but that is a problem with any local method, as far as I
> > understand.

> By non-optimal, I mean not even a local minimum, even in a "convex"
> problem where any local minimum is automatically a global minimum. The
> successive points can get jammed up along a constraint, but at a point
> that is very far from satisfying optimality conditions.

Ah, I can see how penalty methods can help avoid this. Thanks.

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