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Thomas Neidhart commented on MATH828:

Hi Alexey,
I have looked at your updated test case, and my observation is as follows:
You create lots of constraints (L >= 0) that are unnecessary as the solver is already configured
to restrict variables to nonnegative values.
I also think you use the objective function in a wrong way. It is defined as:
{noformat}
c1*x1 + ... cn*xn + d
{noformat}
so at index 0 you have the coefficient for the first variable, .... and the last index is
for the constant term. Now you use something called theta, which you put on index 0 which
is wrong imho.
If I remove all the unnecessary constraints, and move the theta variable to the end of the
objective function vector, the tests run through successfully.
Thomas
> Not expected UnboundedSolutionException
> 
>
> Key: MATH828
> URL: https://issues.apache.org/jira/browse/MATH828
> Project: Commons Math
> Issue Type: Bug
> Affects Versions: 3.0
> Environment: Intel Core i52300 Windows XP SP3
> Reporter: Alexey Slepov
> Labels: linear, math, programming
> Fix For: 3.0
>
> Attachments: ApacheSimplexWrapper.java, ApacheSimplexWrapperTest.java, Entity.java,
commonsmath33.0.jar
>
>
> SimplexSolver throws UnboundedSolutionException when trying to solve minimization linear
programming problem. The number of exception thrown depends on the number of variables.
> In order to see that behavior of SimplexSolver first try to run JUnit test setting a
final variable ENTITIES_COUNT = 2 and that will give almost good result and then set it to
15 and you'll get a massive of unbounded exceptions.
> First iteration is runned with predefined set of input data with which the Solver gives
back an appropriate result.
> The problem itself is well tested by it's authors (mathematicians who I believe know
what they developed) using Matlab 10 with no unbounded solutions on the same rules of creatnig
random variables values.
> What is strange to me is the dependence of the number of UnboundedSolutionException exceptions
on the number of variables in the problem.
> The problem is formulated as
> min(1*t + 0*L) (for every rth subject)
> s.t.
> q(r) + QL >= 0
> x(r)t  XL >= 0
> L >= 0
> where
> r = 1..R,
> L = {l(1), l(2), ..., l(R)} (vector of R rows and 1 column),
> Q  coefficients matrix MxR
> X  coefficients matrix NxR

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