com.imsl.math
Class LinearProgramming

java.lang.Object
  |
  +--com.imsl.math.LinearProgramming

All Implemented Interfaces:

Cloneable, Serializable

public class LinearProgramming

extends Object

implements Serializable, Cloneable

Linear programming problem using the revised simplex algorithm.

Class LinearProgramming uses a revised simplex method to solve linear programming problems, i.e., problems of the form

subject to

where c is the objective coefficient vector, A is the coefficient matrix, and the vectors , , , and are the lower and upper bounds on the constraints and the variables, respectively.

For a complete description of the revised simplex method, see Murtagh (1981) or Murty (1983).

See Also:

Example 1, Example 2, Serialized Form

Nested Class Summary

static class	LinearProgramming.BoundsInconsistentException The bounds given are inconsistent.
static class	LinearProgramming.NumericDifficultyException Numerical difficulty occurred.
static class	LinearProgramming.WrongConstraintTypeException Deprecated. The values for the type of constraint must be either 0, 1 or 2.

Constructor Summary

LinearProgramming(double[][] a, double[] b, double[] c)
Constructor variables of type double.

Method Summary

double[]	getDualSolution() Returns the dual solution.
double	getOptimalValue() Returns the optimal value of the objective function.
double[]	getPrimalSolution() Returns the solution x of the linear programming problem.
void	setConstraintType(int[] constraintType) Sets the types of general constraints in the matrix a.
void	setLowerBound(double[] lowerBound) Sets the upper limit of the constraints.
void	setMaximumIteration(int iterations) Sets the maximum number of iterations.
void	setUpperBound(double[] upperBound) Sets the upper bound on the variables.
void	setUpperLimit(double[] upperLimit) Sets the upper limit of the constraints.
void	solve() Solves the program using the revised simplex algorithm.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

LinearProgramming

public LinearProgramming(double[][] a,
                         double[] b,
                         double[] c)

Constructor variables of type double.

Parameters:

a - A double matrix with coefficients of the constraints

b - A double array containing the right-hand side of the constraints.

c - A double array containing the coefficients of the objective function.

Throws:

IllegalArgumentException - is thrown if the dimensions of a, b.length, and c.length are not consistent.

Method Detail

solve

public final void solve()
                 throws LinearProgramming.BoundsInconsistentException,
                        LinearProgramming.NumericDifficultyException,
                        SingularMatrixException

Solves the program using the revised simplex algorithm.

LinearProgramming.BoundsInconsistentException

LinearProgramming.NumericDifficultyException

SingularMatrixException

setMaximumIteration

public void setMaximumIteration(int iterations)

Sets the maximum number of iterations. Default is set to 10000.

Parameters:

iterations - a int scalar specifying the maximum number of iterations.

setUpperLimit

public void setUpperLimit(double[] upperLimit)

Sets the upper limit of the constraints. If no such constraint exists, then bu is not needed.

Parameters:

upperLimit - a double array containing the upper limit of the constraints that have both the lower and the upper bounds.

setLowerBound

public void setLowerBound(double[] lowerBound)

Sets the upper limit of the constraints. If no such constraint exists, then upper limit is not needed.

setUpperBound

public void setUpperBound(double[] upperBound)

Sets the upper bound on the variables. If there is no upper bound on a variable, then -10e30 should be set as the upper bound.

Parameters:

upperBound - a double array containing the upper bound on the variables.

setConstraintType

public void setConstraintType(int[] constraintType)

Sets the types of general constraints in the matrix a.

Parameters:

constraintType - a int array containing the types of general constraints.

constraintType	Constraint
0
1
2
3

getOptimalValue

public double getOptimalValue()

Returns the optimal value of the objective function.

Returns:

a double scalar containing the optimal value of the objective function.

getPrimalSolution

public double[] getPrimalSolution()

Returns the solution x of the linear programming problem.

Returns:

a double array containing the solution x of the linear programming problem.

getDualSolution

public double[] getDualSolution()

Returns the dual solution.

Returns:

a double array containing the dual solution of the linear programming problem.