[ojAlgo-user] Problems with the quadratic solver

[Joao M. <ma...@gm...>]

Hello,

  My name is Joao Magalhaes, I am an undegraduate student from Brazil.
  I have to solve an optimization problem that has to do with financial
stuff. It can be summarized by the constraint matrix below:


a b c e1 e2 e3 Mean dm1 dm2 dm3    eq1 0,5 2 3 -1





 =  2  eq2 1 -0,5 -2
-1




 =  3  eq3 -0,3 3 -0,8

-1



 =  0  eq4

1 1 1 -3


 =  0  eq5

1

-1 -1

 =  0  eq6


1
-1
-1
 =  0  eq7



1 -1

-1  = 0  eq8 1 1 1                =  1












 objective function: dm1^2 + dm2^2 + dm3^2











 minimize objective function












The goal is to minimize the function dm1^2 + dm2^2 + dm3^2, subject to the
constraints in the matrix (each cell is the factor that multiplies the
variable, when there is no factor, the multiplier is 0).
I searched for Quadratic Solvers in google, and came across ojAlgo. Based on
the javadocs and some source code inspection, I have written the code and
the end of this message. However, I came across two problems:

1) I cannot set quadratic factors for the objective function. I get a
NullPointerException. Inspecting the source code, I concluded that the
objective function must be linear, is this correct? If so, it would be also
possible to model the problem a little bit differently, by adding a new
quadratic constraint and minimizing the new created variable, just as
follows:


Variance  a b c e1 e2 e3 Mean dm1 dm2 dm3

 eq1   0,5 2 3 -1              =  2  eq2   1 -0,5 -2
-1




 =  3  eq3   -0,3 3 -0,8

-1



 =  0  eq4


1 1 1 -3


 =  0  eq5


1

-1 -1

 =  0  eq6



1
-1
-1
 =  0  eq7




1 -1

-1  = 0  eq8   1 1 1






 =  1  eq9 -3                ^2  ^2  ^2  = 0













 Objective function: variance












 minimize variance













However, I tryied this too, but it did not work.

2) In order to keep moving, I used the first model (matrix 1) with 8
equations, but changed the objective function to something linear (just the
sum of the dm variables), so that nothing in the problem is quadratic,
everything is linear. But again, I get a NullPointerException in the
Lagrange Solver:

Exception in thread "main" java.lang.NullPointerException
    at
org.ojalgo.matrix.store.MergedRowsStore.<init>(MergedRowsStore.java:46)
    at
org.ojalgo.optimisation.quadratic.LagrangeSolver.buildIterationSolver(LagrangeSolver.java:56)
    at
org.ojalgo.optimisation.quadratic.LagrangeSolver.performIteration(LagrangeSolver.java:84)
    at
org.ojalgo.optimisation.quadratic.QuadraticSolver.iterate(QuadraticSolver.java:303)
    at
org.ojalgo.optimisation.quadratic.QuadraticSolver.solve(QuadraticSolver.java:275)
    at
org.ojalgo.optimisation.quadratic.QuadraticSolver.solve(QuadraticSolver.java:256)
    at br.com.mindsatwork.ojalgo.test.TestClass.main(TestClass.java:143)


My source code is as follow. Can anyone give me some light on what I am
doing wrong? Please, apologies if this is a very basic question, but it is
the very first time I try ojAlgo. I promise to improve my questions in the
future :-)

Cheers,
Joao Magalhaes

-- ----------------------

import java.math.BigDecimal;
import java.util.HashSet;
import java.util.Set;

import org.ojalgo.optimisation.Expression;
import org.ojalgo.optimisation.ModelValidationException;
import org.ojalgo.optimisation.OptimisationSolver;
import org.ojalgo.optimisation.Variable;
import org.ojalgo.optimisation.OptimisationSolver.Result;
import org.ojalgo.optimisation.quadratic.QuadraticExpressionsModel;


public class Test
{
    public static void main( final String[] args )
        throws ModelValidationException
    {
        final Set<Variable> variables = new HashSet<Variable>();
        final Variable A = new Variable( "A" );
        final Variable B = new Variable( "B" );
        final Variable C = new Variable( "C" );
        final Variable e1 = new Variable( "e1" );
        final Variable e2 = new Variable( "e2" );
        final Variable e3 = new Variable( "e3" );
        final Variable mean = new Variable( "mean" );
        final Variable dm1 = new Variable( "dm1" );
        final Variable dm2 = new Variable( "dm2" );
        final Variable dm3 = new Variable( "dm3" );
        variables.add( A );
        variables.add( B );
        variables.add( C );
        variables.add( e1 );
        variables.add( e2 );
        variables.add( e3 );
        variables.add( mean );
        variables.add( dm1 );
        variables.add( dm2 );
        variables.add( dm3 );

        final QuadraticExpressionsModel model = new
QuadraticExpressionsModel( variables );

        model.addConstraint( "eq1", new BigDecimal( 0 ), new BigDecimal( 0 )
);
        model.addConstraint( "eq2", new BigDecimal( 0 ), new BigDecimal( 0 )
);
        model.addConstraint( "eq3", new BigDecimal( 0 ), new BigDecimal( 0 )
);
        model.addConstraint( "eq4", new BigDecimal( 0 ), new BigDecimal( 0 )
);
        model.addConstraint( "eq5", new BigDecimal( 0 ), new BigDecimal( 0 )
);
        model.addConstraint( "eq6", new BigDecimal( 0 ), new BigDecimal( 0 )
);
        model.addConstraint( "eq7", new BigDecimal( 0 ), new BigDecimal( 0 )
);
        model.addConstraint( "eq8", new BigDecimal( 0 ), new BigDecimal( 0 )
);

        model.getExpression( "eq1" ).setLinearFactor( model.indexOfVariable(
"A" ), new BigDecimal( 0.5 ) );
        model.getExpression( "eq1" ).setLinearFactor( model.indexOfVariable(
"B" ), new BigDecimal( 2 ) );
        model.getExpression( "eq1" ).setLinearFactor( model.indexOfVariable(
"C" ), new BigDecimal( 3 ) );
        model.getExpression( "eq1" ).setLinearFactor( model.indexOfVariable(
"e1" ), new BigDecimal( -1 ) );
        model.getExpression( "eq1" ).setConstant( new BigDecimal( -2 ) );

        model.getExpression( "eq2" ).setLinearFactor( model.indexOfVariable(
"A" ), new BigDecimal( 1 ) );
        model.getExpression( "eq2" ).setLinearFactor( model.indexOfVariable(
"B" ), new BigDecimal( -0.5 ) );
        model.getExpression( "eq2" ).setLinearFactor( model.indexOfVariable(
"C" ), new BigDecimal( -2 ) );
        model.getExpression( "eq2" ).setLinearFactor( model.indexOfVariable(
"e2" ), new BigDecimal( -1 ) );
        model.getExpression( "eq2" ).setConstant( new BigDecimal( -3 ) );

        model.getExpression( "eq3" ).setLinearFactor( model.indexOfVariable(
"A" ), new BigDecimal( -0.3 ) );
        model.getExpression( "eq3" ).setLinearFactor( model.indexOfVariable(
"B" ), new BigDecimal( 3 ) );
        model.getExpression( "eq3" ).setLinearFactor( model.indexOfVariable(
"C" ), new BigDecimal( -0.8 ) );
        model.getExpression( "eq3" ).setLinearFactor( model.indexOfVariable(
"e3" ), new BigDecimal( -1 ) );
        model.getExpression( "eq3" ).setConstant( new BigDecimal( 0 ) );

        model.getExpression( "eq4" ).setLinearFactor( model.indexOfVariable(
"e1" ), new BigDecimal( 1 ) );
        model.getExpression( "eq4" ).setLinearFactor( model.indexOfVariable(
"e2" ), new BigDecimal( 1 ) );
        model.getExpression( "eq4" ).setLinearFactor( model.indexOfVariable(
"e3" ), new BigDecimal( 1 ) );
        model.getExpression( "eq4" ).setLinearFactor( model.indexOfVariable(
"mean" ), new BigDecimal( -3 ) );
        model.getExpression( "eq4" ).setConstant( new BigDecimal( 0 ) );

        model.getExpression( "eq5" ).setLinearFactor( model.indexOfVariable(
"e1" ), new BigDecimal( 1 ) );
        model.getExpression( "eq5" ).setLinearFactor( model.indexOfVariable(
"mean" ), new BigDecimal( -1 ) );
        model.getExpression( "eq5" ).setLinearFactor( model.indexOfVariable(
"dm1" ), new BigDecimal( -1 ) );
        model.getExpression( "eq5" ).setConstant( new BigDecimal( 0 ) );

        model.getExpression( "eq6" ).setLinearFactor( model.indexOfVariable(
"e2" ), new BigDecimal( 1 ) );
        model.getExpression( "eq6" ).setLinearFactor( model.indexOfVariable(
"mean" ), new BigDecimal( -1 ) );
        model.getExpression( "eq6" ).setLinearFactor( model.indexOfVariable(
"dm2" ), new BigDecimal( -1 ) );
        model.getExpression( "eq6" ).setConstant( new BigDecimal( 0 ) );

        model.getExpression( "eq7" ).setLinearFactor( model.indexOfVariable(
"e3" ), new BigDecimal( 1 ) );
        model.getExpression( "eq7" ).setLinearFactor( model.indexOfVariable(
"mean" ), new BigDecimal( -1 ) );
        model.getExpression( "eq7" ).setLinearFactor( model.indexOfVariable(
"dm3" ), new BigDecimal( -1 ) );
        model.getExpression( "eq7" ).setConstant( new BigDecimal( 0 ) );

        model.getExpression( "eq8" ).setLinearFactor( model.indexOfVariable(
"A" ), new BigDecimal( 1 ) );
        model.getExpression( "eq8" ).setLinearFactor( model.indexOfVariable(
"B" ), new BigDecimal( 1 ) );
        model.getExpression( "eq8" ).setLinearFactor( model.indexOfVariable(
"C" ), new BigDecimal( 1 ) );
        model.getExpression( "eq8" ).setConstant( new BigDecimal( -1 ) );

        final Expression obj = model.getObjectiveExpression();

        obj.setLinearFactor( model.indexOfVariable( "dm1" ), new BigDecimal(
1 ) );
        obj.setLinearFactor( model.indexOfVariable( "dm2" ), new BigDecimal(
1 ) );
        obj.setLinearFactor( model.indexOfVariable( "dm3" ), new BigDecimal(
1 ) );

        // obj.setQuadraticFactor( model.indexOfVariable( "dm1" ),
model.indexOfVariable( "dm1" ),
        // new BigDecimal( 1 ) );
        // obj.setQuadraticFactor( model.indexOfVariable( "dm2" ),
model.indexOfVariable( "dm2" ),
        // new BigDecimal( 1 ) );
        // obj.setQuadraticFactor( model.indexOfVariable( "dm3" ),
model.indexOfVariable( "dm3" ),
        // new BigDecimal( 1 ) );

        model.setMaximisation( false );
        model.setMinimisation( true );

        final OptimisationSolver solver = model.getDefaultSolver();

        final Result res = solver.solve();

        System.out.println( res.getState().toString() );
        System.out.println( res.toString() );
    }

}