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From Debasish Das <debasish.da...@gmail.com>
Subject Re: apply simplex method to fix linear programming in spark
Date Wed, 04 Nov 2015 21:50:13 GMT
```Yeah for this you can use breeze quadratic minimizer...that's integrated
with spark in one of my spark pr.

You have quadratic objective with equality which is primal and your
proximal is positivity that we already support. I have not given an API for
linear objective but that should be simple to add. You can add an issue in
breeze for the enhancememt.

Alternatively you can use breeze lpsolver as well that uses simplex from
apache math.
On Nov 4, 2015 1:05 AM, "Zhiliang Zhu" <zchl.jump@yahoo.com> wrote:

> Hi Debasish Das,
>
> Firstly I must show my deep appreciation towards you kind help.
>
> Yes, my issue is some typical LP related, it is as:
> Objective function:
> f(x1, x2, ..., xn) = a1 * x1 + a2 * x2 + ... + an * xn,   (n would be some
> number bigger than 100)
>
> There are only 4 constraint functions,
> x1 + x2 + ... + xn = 1,                             1)
> b1 * x1 + b2 * x2 + ... + bn * xn = b,         2)
> c1 * x1 + c2 * x2 + ... + cn * xn = c,         3)
> x1, x2, ..., xn >= 0 .
>
> To find the solution of x which lets objective function the biggest.
>
> Since simplex method may not be supported by spark. Then I may switch to
> the way as, since the likely solution x must be on the boundary of 1), 2)
> and 3) geometry,
> that is to say, only three xi may be >= 0, all the others must be 0.
> Just look for all that kinds of solutions of 1), 2) and 3), the number
> would be C(n, 3) + C(n, 2) + C(n, 1), at last to select the most optimized
> one.
>
> Since the constraint number is not that large, I think this might be some
> way.
>
> Thank you,
> Zhiliang
>
>
> On Wednesday, November 4, 2015 2:25 AM, Debasish Das <
> debasish.das83@gmail.com> wrote:
>
>
> Spark has nnls in mllib optimization. I have refactored nnls to breeze as
> well but we could not move out nnls from mllib due to some runtime issues
> from breeze.
> Issue in spark or breeze nnls is that it takes dense gram matrix which
> does not scale if rank is high but it has been working fine for nnmf till
> 400 rank.
> I agree with Sean that you need to see if really simplex is needed. Many
> constraints can be formulated as proximal operator and then you can use
> breeze nonlinearminimizer or spark-tfocs package if it is stable.
> On Nov 2, 2015 10:13 AM, "Sean Owen" <sowen@cloudera.com> wrote:
>
> I might be steering this a bit off topic: does this need the simplex
> method? this is just an instance of nonnegative least squares. I don't
> think it relates to LDA either.
>
> Spark doesn't have any particular support for NNLS (right?) or simplex
> though.
>
> On Mon, Nov 2, 2015 at 6:03 PM, Debasish Das <debasish.das83@gmail.com>
> wrote:
> > Use breeze simplex which inturn uses apache maths simplex...if you want
> to
> > use interior point method you can use ecos
> > https://github.com/embotech/ecos-java-scala ...spark summit 2014 talk on
> > quadratic solver in matrix factorization will show you example
> integration
> > with spark. ecos runs as jni process in every executor.
> >
> > On Nov 1, 2015 9:52 AM, "Zhiliang Zhu" <zchl.jump@yahoo.com.invalid>
> wrote:
> >>
> >> Hi Ted Yu,
> >>
> >> Thanks very much for your kind reply.
> >> Do you just mean that in spark there is no specific package for simplex
> >> method?
> >>
> >> Then I may try to fix it by myself, do not decide whether it is
> convenient
> >> to finish by spark, before finally fix it.
> >>
> >> Thank you,
> >> Zhiliang
> >>
> >>
> >>
> >>
> >> On Monday, November 2, 2015 1:43 AM, Ted Yu <yuzhihong@gmail.com>
> wrote:
> >>
> >>
> >> A brief search in code base shows the following:
> >>
> >>     TODO: Add simplex constraints to allow alpha in (0,1).
> >> ./mllib/src/main/scala/org/apache/spark/mllib/clustering/LDA.scala
> >>
> >> I guess the answer to your question is no.
> >>
> >> FYI
> >>
> >> On Sun, Nov 1, 2015 at 9:37 AM, Zhiliang Zhu
> <zchl.jump@yahoo.com.invalid>
> >> wrote:
> >>
> >> Dear All,
> >>
> >> As I am facing some typical linear programming issue, and I know simplex
> >> method is specific in solving LP question,
> >> I am very sorry that whether there is already some mature package in
> spark
> >> about simplex method...
> >>
> >> Thank you very much~
> >> Best Wishes!
> >> Zhiliang
> >>
> >>
> >>
> >>
> >>
> >
>
>
>
>

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