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https://issues.apache.org/jira/browse/MATH-828?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13419013#comment-13419013
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Alexey Slepov commented on MATH-828:
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Thomas, thanks for reference that the solver is already configured to restrict
variables to non-negative values. That signally decreased time the solver
needed to find solution as much as decreased the number of
UnboundedSolutionExceptions.
As to the objective, there is a misunderstanding I believe.
I use the definition of the objective as it's declared in
http://commons.apache.org/math/apidocs/org/apache/commons/math/optimization/linear/LinearObjectiveFunction.html
and theta is x1 and there are R+1 variables. R is the number of objects the
omtimum is to find for (ENTITIES_COUNT) that is equal to the number of lambdas
l(i). And as it shown in the very first test of the JUnit test where Q = [1,2],
X = [2,1] and L = T[l1, l2] the solver gives an expected result. That is the
indicator that equations are written properly. In other words for every single
of N entities there has to be an objective with N + 1 variables. For the case
of 2 entities the 3 dimension space is used to build a surface that has it's
theta or x(1) coordinate set to minimum, for the case of 3 entities the 4
dimension space is used to build a shape that has it's theta or x(1) coordinate
set to minimum and etc.
Here is how it looks for the simplest case (JUnit test #0)
Model name: DEA problem
t L1 L2
Minimize 1 0 0
R1 0 2 1 >= 1
R2 2 -1 -2 >= 0
R3 0 1 0 >= 0
R4 0 0 1 >= 0
Type Real Real Real
upbo Inf Inf Inf
lowbo 0 0 0
the objective is to be 0.25 and theta = 0.25 and L1 = 0.5, L2 = 0
The solver gives the same result for the case.
But only I add more entities to find minimum for as the same add more lambdas
the solver gives back wrong answer, unbounded solution or theta greater than 1
(that is wrong due to the problem condition)
I'm sure it's been really too early to close the issue :(
> Not expected UnboundedSolutionException
> ---------------------------------------
>
> Key: MATH-828
> URL: https://issues.apache.org/jira/browse/MATH-828
> Project: Commons Math
> Issue Type: Bug
> Affects Versions: 3.0
> Environment: Intel Core i5-2300 Windows XP SP3
> Reporter: Alexey Slepov
> Labels: linear, math, programming
> Fix For: 3.0
>
> Attachments: ApacheSimplexWrapper.java,
> ApacheSimplexWrapperTest.java, Entity.java, commons-math3-3.0.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 r-th 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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