fix bug in documentation of find_minimum_on_interval

[williamstein]

From Thomas Savitsky (on sage-devel):
> > I've noticed that the function find_minimum_on_interval makes no attempt to
> > find "the" minimum on the interval as the documentation implies, but rather
> > "a local" minimum.  I imagine this may be a source of confusion for other
> > new users as well.  Rather than treating this as a bug, may I suggest
> > changing the documentation for this function to reflect that it only finds a
> > local minimum and adding an additional function which searches for a global
> > minimum?
>
> +1  Can you provide a few examples for the docstring that illustrate this?

Do these work?

sage: h(x) =  -sin(x) - 2*sin(2*x)
sage: h.find_minimum_on_interval(0, 2*pi)
(-1.3271810224585345, 3.8298351449342838)
But there is another local minimum at h(0.8666760871050464) = -2.73581510406


sage: find_minimum_on_interval(x*(x-1)*(x+1), -2, 2)
(-0.38490017945975047, 0.57735026913115706)
The minimum on this interval is the endpoint h(-2) = 6.


sage: find_minimum_on_interval((x-2)*(x-1)*x*(x+1) - x, -2, 2)
(-0.43749999999999994, -0.49999999973911674)

but
sage: find_minimum_on_interval((x-2)*(x-1)*x*(x+1) - x, 0, 2)
(-2.6642135623730949, 1.7071067879138031)

}}}[[BR]]

CC: @kcrisman

Component: calculus

Keywords: sd31

Reviewer: Karl-Dieter Crisman, Burcin Erocal

Issue created by migration from https://trac.sagemath.org/ticket/5960

[burcin]

comment:1

The real problem is described in #2607. I suggest we fix that instead of changing the documentation to justify this behavior.

If people think it necessary, we can create another function called .find_local_minimum() with the current behavior.

Note that I haven't looked at the code at all, and it's possible that I'm missing the point entirely.

[kcrisman]

Changed keywords from none to sd31

[kcrisman]

comment:3

This Scipy tutorial page should be relevant. I will try to resolve this soon.

[kcrisman]

comment:4

sage: from scipy import optimize
sage: optimize.fminbound(h._fast_float_(x),0,6,full_output=True)
(3.8298366870225147, -1.327181022449951, 0, 10)
sage: optimize.fminbound(h._fast_float_(x),0,3,full_output=True)
(0.86667541098916612, -2.7358151040622416, 0, 9)

From the tutorial referenced above:

Finds a local minimizer 

so I agree this should be closed as a dup.

Moving examples there.

[kcrisman]

Reviewer: Karl-Dieter Crisman, Burcin Erocal

[kcrisman]

comment:5

To release manager - please close as a duplicate of #2607.