Package com.imsl.math

Class DenseLP

java.lang.Object
com.imsl.math.DenseLP
All Implemented Interfaces:
Serializable, Cloneable
public class DenseLP extends Object implements Serializable, Cloneable
Solves a linear programming problem using an active set strategy.

Class DenseLP uses an active set strategy to solve linear programming problems, i.e., problems of the form

$$\mathop {\min }\limits_{x\; \in \;R^n } c^T x$$

subject to

$$b_l \le Ax \le b_u$$

$$\,\,x_l \le x \le x_u$$

where c is the objective coefficient vector, A is the coefficient matrix, and the vectors \(b_l\), \(b_u\), \(x_l\), and \(x_u\) are the lower and upper bounds on the constraints and the variables, respectively.

If the linear constraints are infeasible an \(L_1\) solution to the constraints are used as a replacement for the stated constraints. An exception is thrown but a generalized solution is computed and available using methods getPrimalSolution or getDualSolution. Similar comments hold for any of the three additional conditions: (1) There are multiple solutions; (2) some constraints are discarded, or (3) cycling in the algorithm is identified.

Refer to the following paper for further information:

Krogh, Fred, T. (2005), see An Algorithm for Linear Programming http://mathalacarte.com/fkrogh/pub/lp.pdf

See Also:

  • Constructor Details

    • DenseLP

      public DenseLP(MPSReader mps)
      Constructor using an MPSReader object.
      Parameters:
      mps - An MPSReader object specifying the Linear Programming problem.
      Throws:
      IllegalArgumentException - is thrown if the problem dimensions are not consistent.

    • DenseLP

      public DenseLP(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 Details

    • clone

      public Object clone()
      Creates and returns a copy of this object.
      Overrides:
      clone in class Object

    • solve

      public final void solve() throws DenseLP.BoundsInconsistentException, DenseLP.NoAcceptablePivotException, DenseLP.ProblemUnboundedException, DenseLP.ProblemVacuousException, DenseLP.AllConstraintsNotSatisfiedException, DenseLP.MultipleSolutionsException, DenseLP.SomeConstraintsDiscardedException, DenseLP.CyclingOccurringException, DenseLP.NoConstraintsAvailableException
      Solves the problem using an active set method. solve must be invoked prior to calling any of the "get" methods.
      Throws:
      DenseLP.BoundsInconsistentException - is thrown if the bounds are inconsistent.
      DenseLP.NoAcceptablePivotException - is thrown if an acceptable pivot could not be found.
      DenseLP.ProblemUnboundedException - is thrown if there is no finite solution to the problem.
      DenseLP.ProblemVacuousException - is thrown if the problem is vacuous.
      DenseLP.AllConstraintsNotSatisfiedException - is thrown if all constraints are not satisfied.
      DenseLP.MultipleSolutionsException - is thrown if the problem has multiple solutions.
      DenseLP.SomeConstraintsDiscardedException - is thrown if some constraints were discarded because they were too linearly dependent on other active constraints.
      DenseLP.CyclingOccurringException - is thrown if the algorithm appears to be cycling.
      DenseLP.NoConstraintsAvailableException - is thrown if all constraints are of constraint type 4.

    • setRefinementType

      public void setRefinementType(int iRefinement)
      Set the type of refinement used.
      Parameters:
      iRefinement - An int scalar value which defines the type of refinement to be used. The possible settings are:
      iRefinementAction
      0 No refinement. Always compute dual. Default.
      1 Iterative refinement.
      2 Use extended refinement. Iterate until no more progress.

      If refinement is used, the coefficient matrices and other data are saved at the beginning of the computation. When finished this data together with the solution obtained is checked for consistency. If the discrepancy is too large, the solution process is restarted using the problem data just after processing the equalities, but with the final x values and final active set.

    • setUpperLimit

      public void setUpperLimit(double[] upperLimit)
      Sets the upper limit of the constraints.
      Parameters:
      upperLimit - a double array containing the upper limit, \(b_u\), of the constraints.

    • setLowerBound

      public void setLowerBound(double[] lowerBound)
      Sets the lower bound, \(x_l\), on the variables. If there is no lower bound on a variable, then 1.0e30 should be set as the lower bound.
      Parameters:
      lowerBound - a double array containing the lower bound on the variables. Default = 0.

    • setUpperBound

      public void setUpperBound(double[] upperBound)
      Sets the upper bound, \(x_u\), on the variables. If there is no upper bound on a variable, then -1.0e30 should be set as the upper bound.
      Parameters:
      upperBound - a double array containing the upper bound on the variables. The default is no upper bound.

    • setConstraintType

      public void setConstraintType(int[] constraintType)
      Sets the types of general constraints in the matrix a.
      Parameters:
      constraintType - an int array containing the types of general constraints. Let \( r_i=a_{i1}x_1+...+a_{in}x_n\). Then the value of constraintType[i] signifies the following:

      constraintType

      Constraint
      0 \({\rm {r}}_i = {\rm {b}}_i\)
      1 \({\rm {r}}_i \le {\rm {b}}_i \,\,\, or \,\,\, {\rm {r}}_i \le {\rm {b}}_{{\rm {u}}_i} \,\,\, if \,\,supplied\)
      2 \({\rm {r}}_i \ge {\rm {b}}_i\)
      3 \({\rm {b}}_i \le {\rm {r}}_i \le {\rm {b}}_{{\rm {u}}_i}\)
      4 Ignore this constraint

      Default=0.

    • getOptimalValue

      public double getOptimalValue()
      Returns the optimal value of the objective function.
      Returns:
      a double scalar containing the optimal value of the objective function. If a solution has not been computed, Double.NaN is returned.

    • getIterationCount

      public int getIterationCount()
      Returns the iteration count.
      Returns:
      an int scalar containing the iteration count.

    • 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.