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From Zhiliang Zhu <zchl.j...@yahoo.com.INVALID>
Subject Re: apply simplex method to fix linear programming in spark
Date Wed, 04 Nov 2015 09:01:55 GMT
```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,
>>
>> 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
>>
>>
>> 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
>>
>> Thank you very much~
>> Best Wishes!
>> Zhiliang
>>
>>
>>
>>
>>
>

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