Package com.imsl.math

Class MinConNonlin

java.lang.Object
com.imsl.math.MinConNonlin
All Implemented Interfaces:
Serializable, Cloneable
public class MinConNonlin extends Object implements Serializable, Cloneable
Deprecated.
MinConNonlin has been replaced by MinConNLP.
General nonlinear programming solver.

MinConNonlin is based on the following FORTRAN subroutines licensed from Prof. Dr. K. Schittkowski (1986) by agreement dated 12/2/1985: NLPQL, NLPQL, MERIT, LINSEA, QL, LDL. More recent versions on these routines are available from Dr. Schittkowski.

$$\mathop {\min }\limits_{x\; \in \;R^n } f\left( x \right)$$

subject to

$${\rm{ }}g_j \left( x \right) = 0, {\rm{for}} \,\, j = 1,\; \ldots ,\;m_e$$

$$g_j \left( x \right) \ge 0, \rm{for} \,\, {j = m_e + 1,\; \ldots ,\;m}$$

$$x_l \le x \le x_u$$

where all problem functions are assumed to be continuously differentiable. The method, based on the iterative formulation and solution of quadratic programming (QP) subproblems, obtains these subproblems by using a quadratic approximation of the Lagrangian and by linearizing the constraints. That is,

$$\mathop {\min }\limits_{x\; \in \;R^n } \frac{1}{2}d^T B_k d + \nabla f\left( {x_k } \right)^T d$$

subject to

$$\nabla g_j \left( {x_k } \right)^T d + g_j \left( {x_k } \right) = 0,{\rm{for}} \,\, j = 1,\; \ldots ,\;m_e$$

$$\nabla g_j \left( {x_k } \right)^T d + g_j \left( {x_k } \right) \ge 0, {\rm{for}} \,\, j = m_e + 1,\; \ldots ,\;m$$

$$x_l - x_k \le d \le x_u - x_k$$

where \(B_k\) is a positive definite approximation of the Hessian, and \(x_k\) is the current iterate. Let \(d_k\) be the solution of the subproblem. A line search is used to find a new point \(x_{k+1}\),

$$x_{k + 1} = x_k + \lambda d_k \,\,\,\,\lambda \in \left( {0,1} \right]$$

such that a "merit function" will have a lower function value at the new point. Here, the augmented Lagrange function (Schittkowski 1986) is used as the merit function.

When optimality is not achieved, \(B_k\) is updated according to the modified BFGS formula (Powell 1978). Note that this algorithm may generate infeasible points during the solution process. Therefore, if feasibility must be maintained for intermediate points, this function may not be suitable. For more theoretical and practical details, see Stoer (1985), Schittkowski (1980, 1983, 1986) and Gill et al. (1985).

See Also:

  • Constructor Details

    • MinConNonlin

      public MinConNonlin(int mTotalConstraints, int mEqualityConstraints, int nVariables) throws IllegalArgumentException
      Deprecated.
      Nonlinear programming solver constructor.
      Parameters:
      mTotalConstraints - An int scalar value which defines the total number of constraints
      mEqualityConstraints - An int scalar value which defines the number of equality constraints
      nVariables - An int scalar value which defines the number of variables.
      Throws:
      IllegalArgumentException

  • Method Details

    • solve

      public double[] solve(MinConNonlin.Function F) throws MinConNonlin.UphillSearchCalcException, MinConNonlin.LineSearchException, MinConNonlin.TooManyIterationsException, MinConNonlin.ZeroSearchDirectionException, MinConNonlin.QPConstraintsException
      Deprecated.
      Solve a general nonlinear programming problem using the successive quadratic programming algorithm with a finite-difference gradient or with a user-supplied gradient.
      Parameters:
      F - defines the user-supplied function to evaluate the function at a given point. F can be used to supply a gradient of the function. If F implements Gradient the user-supplied gradient is used. Otherwise,an attempt to solve the problem is made using a finite-difference gradient.
      Returns:
      a double array containing the solution of the nonlinear programming problem.
      Throws:
      MinConNonlin.UphillSearchCalcException
      MinConNonlin.LineSearchException
      MinConNonlin.TooManyIterationsException
      MinConNonlin.ZeroSearchDirectionException
      MinConNonlin.QPConstraintsException

    • setGuess

      public void setGuess(double[] xguess)
      Deprecated.
      Set the initial guess of the minimum point of the input function. If this member function is not called, the elements of this array are set to 0.0..
      Parameters:
      xguess - a double array specifying the initial guess of the minimum point of the input function

    • setXscale

      public void setXscale(double[] xscale)
      Deprecated.
      Set the diagonal scaling matrix for the variables. If this member function is not called, the elements of this array are set to 1.0..
      Parameters:
      xscale - a double array specifying the diagonal scaling matrix for the variables
      Throws:
      IllegalArgumentException - is thrown if any of the elements of xscale is less than or equal to 0

    • setXlowerBound

      public void setXlowerBound(double[] xlb)
      Deprecated.
      Set the lower bounds on the variables. If this member function is not called, the elements of this array are set to -1.0e6.
      Parameters:
      xlb - a double array specifying the lower bounds on the variables

    • setXupperBound

      public void setXupperBound(double[] xub)
      Deprecated.
      Set the upper bounds on the variables. If this member function is not called, the elements of this array are set to 1.0e6.
      Parameters:
      xub - a double array specifying the upper bounds on the variables

    • setAccuracy

      public void setAccuracy(double acc)
      Deprecated.
      Set the final accuracy. If this member function is not called, acc is set to 1.7e-8.
      Parameters:
      acc - a double scalar value specifying the final accuracy.
      Throws:
      IllegalArgumentException - is thrown if acc is less than or equal to 0.0

    • setScalingVariable

      public void setScalingVariable(double scbnd)
      Deprecated.
      Set the scaling variable for the problem function. If this member function is not called, scbnd is set to 1.0e3.
      Parameters:
      scbnd - a double scalar value specifying the scaling variable for the problem function.
      Throws:
      IllegalArgumentException - is thrown if scbnd is less than or equal to 0.0

    • setMaxIterations

      public void setMaxIterations(int maxIterations)
      Deprecated.
      Set the maximum number of iterations allowed. If this member function is not called, the maximum number of iterations is set to 100.
      Parameters:
      maxIterations - an int specifying the maximum number of iterations allowed
      Throws:
      IllegalArgumentException - is thrown if maxIterations is less than or equal to 0