MinConNonlin (JMSL Numerical Library (jmsl) 2021.0.0 API)

java.lang.Object
- com.imsl.math.MinConNonlin

All Implemented Interfaces:

Serializable, Cloneable

Deprecated.
MinConNonlin has been replaced by MinConNLP.
```
public class MinConNonlin
extends Object
implements Serializable, Cloneable
```
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:

Finite-difference Example, Gradient Example, Serialized Form

Nested Class Summary

Nested Classes
Modifier and Type	Class and Description
`static interface`	`MinConNonlin.Function` Deprecated. `MinConNonlin` has been replaced by `MinConNLP`.
`static interface`	`MinConNonlin.Gradient` Deprecated. `MinConNonlin` has been replaced by `MinConNLP`.
`static class`	`MinConNonlin.LineSearchException` Deprecated. `MinConNonlin` has been replaced by `MinConNLP`.
`static class`	`MinConNonlin.QPConstraintsException` Deprecated. `MinConNonlin` has been replaced by `MinConNLP`.
`static class`	`MinConNonlin.TooManyIterationsException` Deprecated. `MinConNonlin` has been replaced by `MinConNLP`.
`static class`	`MinConNonlin.UphillSearchCalcException` Deprecated. `MinConNonlin` has been replaced by `MinConNLP`.
`static class`	`MinConNonlin.ZeroSearchDirectionException` Deprecated. `MinConNonlin` has been replaced by `MinConNLP`.

Constructor Summary

Constructors
Constructor and Description
`MinConNonlin(int mTotalConstraints, int mEqualityConstraints, int nVariables)` Deprecated. Nonlinear programming solver constructor.

Method Summary

All Methods Instance Methods Concrete Methods Deprecated Methods
Modifier and Type	Method and Description
`void`	`setAccuracy(double acc)` Deprecated. Set the final accuracy.
`void`	`setGuess(double[] xguess)` Deprecated. Set the initial guess of the minimum point of the input function.
`void`	`setMaxIterations(int maxIterations)` Deprecated. Set the maximum number of iterations allowed.
`void`	`setScalingVariable(double scbnd)` Deprecated. Set the scaling variable for the problem function.
`void`	`setXlowerBound(double[] xlb)` Deprecated. Set the lower bounds on the variables.
`void`	`setXscale(double[] xscale)` Deprecated. Set the diagonal scaling matrix for the variables.
`void`	`setXupperBound(double[] xub)` Deprecated. Set the upper bounds on the variables.
`double[]`	`solve(MinConNonlin.Function F)` Deprecated. Solve a general nonlinear programming problem using the successive quadratic programming algorithm with a finite-difference gradient or with a user-supplied gradient.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Constructor Detail
  - 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 Detail
  - 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

Class MinConNonlin

Nested Class Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

MinConNonlin

Method Detail

solve

setGuess

setXscale

setXlowerBound

setXupperBound

setAccuracy

setScalingVariable

setMaxIterations