[ojAlgo-user] Problems with the quadratic solver (format problems fixed)

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

Hello again,

   Looks like the matrix got messed up in my previous post. So, I am
sending the message again, but with the equations instead of the
matrix.
  Apologies for this.
  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 equations below:

Constraints:

eq1: 0.5*a + 2*b + 3*c - e1 = 2
eq2: a - 0.5*b - 2*c - e2 = 3
eq3: -0.3*a + 3*c - e3 = 0
eq4: e1 + e2 + e3 - 3*mean = 0
eq5: e1 - mean - dm1 = 0
eq6: e2 - mean - dm2 = 0
eq7: e3 - mean - dm3 = 0
eq8: a + b + c = 1

Objective: minimize dm1^2 + dm2^2 + dm3^2

The goal is to minimize the function dm1^2 + dm2^2 + dm3^2, subject to
the constraints.
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:

eq1: 0.5*a + 2*b + 3*c - e1 = 2
eq2: a - 0.5*b - 2*c - e2 = 3
eq3: -0.3*a + 3*c - e3 = 0
eq4: e1 + e2 + e3 - 3*mean = 0
eq5: e1 - mean - dm1 = 0
eq6: e2 - mean - dm2 = 0
eq7: e3 - mean - dm3 = 0
eq8: a + b + c = 1
eq9: 3* var - dm1^2 - dm2^2 - dm3^2 = 0

Objective: minimize var

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

2) In order to keep moving on, I used the first model 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 follows. 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() );
    }

}