R help - May 2021 - Testing optimization solvers with equality constraints

Yes. "*on* the unit sphere" means on the surface, as you can guess
from the equality constraint. And 'auglag()' does find the minimum, so
no need for a special approach.

I was/am interested in why all these other good solvers get stuck,
i.e., do not move away from the starting point. And how to avoid this
in general, not only for this specific example.


On Sat, 22 May 2021 at 09:44, Abby Spurdle <spurdle.a at gmail.com>
wrote:
>
> Sorry, this might sound like a poor question:
> But by "on the unit sphere", do you mean on the ***surface*** of
the sphere?
> In which case, can't the surface of a sphere be projected onto a pair
> of circles?
> Where the cost function is reformulated as a function of two (rather
> than three) variables.
>

For a start, there's two local minima.

Add to that floating point errors.
And possible assumptions by the package authors.

----begin code----
f <- function (x, y, sign)
{   unsign.z <- sqrt (1 - x^2 - y^2)
    2 * (x^2 - sign * y * unsign.z)
}

north.f <- function (x, y) f (x, y, +1)
south.f <- function (x, y) f (x, y, -1)

N <- 100
p0 <- par (mfrow = c (1, 2) )
plotf_cfield (north.f, c (-1.1, 1.1),
    main="north",
    ncontours=10, n=N, raster=TRUE, hcv=TRUE)
plotf_cfield (south.f, c (-1.1, 1.1),
    main="south",
    ncontours=10, n=N, raster=TRUE, hcv=TRUE)
par (p0)
----end code ----

Please ignore R warnings.
I'm planning to reinvent this package soon.
And also, it wasn't designed for circular heatmaps.


On Sat, May 22, 2021 at 8:02 PM Hans W <hwborchers at gmail.com>
wrote:
>
> Yes. "*on* the unit sphere" means on the surface, as you can
guess
> from the equality constraint. And 'auglag()' does find the minimum,
so
> no need for a special approach.
>
> I was/am interested in why all these other good solvers get stuck,
> i.e., do not move away from the starting point. And how to avoid this
> in general, not only for this specific example.
>
>
> On Sat, 22 May 2021 at 09:44, Abby Spurdle <spurdle.a at gmail.com>
wrote:
> >
> > Sorry, this might sound like a poor question:
> > But by "on the unit sphere", do you mean on the
***surface*** of the sphere?
> > In which case, can't the surface of a sphere be projected onto a
pair
> > of circles?
> > Where the cost function is reformulated as a function of two (rather
> > than three) variables.
> >
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