e04ryf : NAG Library, Mark 26

e04ryf is a part of the NAG optimization modelling suite. It allows you to print information about the problem, stored as a handle, such as which parts have already been defined or details of the matrix constraints.

#include <nagmk26.h>

e04ryf prints information on a problem handle which has been previously initialized by e04raf. Various pieces of information can be retrieved and printed to the given output unit. This can be helpful when the routine is interfaced from interactive environments, for debugging purposes or to help familiarize you with the NAG optimization modelling suite.

The printer is guided by a command string which contains one or more of the following keywords:

Overview: Gives a brief overview of the problem handle, particularly, which phase it is in, if the problem or optional parameters can be edited and which parts of the problem have already been set. This might be helpful to clarify situations when $ifail = 2$ or $3$ (the problem cannot be altered anymore, a certain part has already been defined) is obtained from routines, such as, e04ref, e04rff, e04rhf and e04rjf.
Objective: Prints the objective function as it was defined by e04ref or e04rff if it is linear or quadratic. Prints the sparsity structure of the objective function as it was defined by e04rgf if it is nonlinear or nonlinear least squares by e04rmf.
Simple bounds: Prints the variable bounds as defined by e04rhf. This might help you understand the effect of the optional parameter Infinite Bound Size on the bounds.
Linear constraints bounds
Linear constraints detailed: Print bounds or linear constraint matrix as defined by e04rjf.
Matrix constraints: Gives a list of the matrix constraints as defined by e04rnf and e04rpf. For each matrix constraint its idblk, dimension and order (e.g., linear, bilinear) are printed.
Matrix constraints detailed: Prints all the matrix constraints including all nonzeros of all the matrices as formulated by e04rnf and e04rpf.
Nonlinear constraints bounds
Nonlinear constraints detailed: Print bounds or sparsity structure of the nonlinear constraints as defined by e04rkf.
Multipliers sizes: Prints the expected dimensions of arrays storing the Lagrangian multipliers, such as u and ua of the solver e04svf which store the Lagrangian multipliers for standard and matrix constraints, respectively. This might be helpful in particular in connection with Overview and Matrix constraints to check the way the sizes of the arrays are derived.
Options: Prints all the current optional parameters. It flags whether the argument is at its default choice, whether you have set it or whether it is chosen by the solver (for example, options left on ‘AUTO’ setting after the solver has been called).

Note that the output data might not match your input exactly. The sparse matrices are typically transposed, sorted and explicit zeros removed and in certain cases transformed as needed (for example, matrices

Q_{i j}

and

Q_{j i}

are merged by e04rpf).

On entry: the handle to the problem. It needs to be initialized by e04raf and must not be changed.

On entry: the Fortran unit number which identifies the file to be written to.

Constraint:

nout \geq 0

On entry: a command string which contains one or more keywords which identify the piece of information about the handle to be printed. Keywords are case-insensitive and space tolerant. Multiple keywords in cmdstr must be separated by commas or semicolons.

Constraint: cmdstr can only contain one or more of the following accepted keywords: overview, objective, simple bounds, linear constraints bounds, linear constraints detailed, matrix constraints, matrix constraints detailed, nonlinear constraints bounds, nonlinear constraints detailed, multipliers sizes, options.

On entry: ifail must be set to

0

- 1 or 1

. If you are unfamiliar with this argument you should refer to Section 3.4 in How to Use the NAG Library and its Documentation for details.

For environments where it might be inappropriate to halt program execution when an error is detected, the value

- 1 or 1

is recommended. If the output of error messages is undesirable, then the value

1

is recommended. Otherwise, if you are not familiar with this argument, the recommended value is

0

. When the value $- 1 or 1$ is used it is essential to test the value of ifail on exit.

On exit:

ifail = 0

unless the routine detects an error or a warning has been flagged (see Section 6).

If on entry

ifail = 0

- 1

, explanatory error messages are output on the current error message unit (as defined by x04aaf).

Errors or warnings detected by the routine:

The supplied handle does not define a valid handle to the data structure for the NAG optimization modelling suite. It has not been initialized by e04raf or it has been corrupted.

On entry,

nout = 〈value〉

.
Constraint:

nout \geq 0

cmdstr does not contain any keywords or is empty.

Keyword number

〈value〉

is not recognized, it is too long.

Keyword number

〈value〉

is not recognized.

An error occurred when writing to output.

An unexpected error has been triggered by this routine. Please contact NAG.

See Section 3.9 in How to Use the NAG Library and its Documentation for further information.

Your licence key may have expired or may not have been installed correctly.

See Section 3.8 in How to Use the NAG Library and its Documentation for further information.

Dynamic memory allocation failed.

See Section 3.7 in How to Use the NAG Library and its Documentation for further information.

e04ryf is not threaded in any implementation.

This example shows the life-cycle of a handle of a typical (BMI-SDP) problem by printing the overview of the handle in various stages of the problem formulation and after the solution is found. It is also helpful to notice how a linear matrix inequality is extended with the bilinear term, see e04raf and e04rpf for further details.

The problem is as follows:

\begin{array}{l} \underset{x, y ​ ​ \in ​ ​ ℝ}{minimize} & y \\ subject to & (\begin{matrix} 1 & x - 1 & y \\ x - 1 & 3 / 4 & 0 \\ y & 0 & 16 \end{matrix}) ⪰ 0 \\ (\begin{matrix} x & - x y \\ - x y & 1 \end{matrix}) ⪰ 0 \\ x \geq 0 \\ - 3 \leq y \leq 3 \end{array}

The solution is

x = 1 / 4

y = - 2

Note that the matrix constraints need to be supplied in the form of equation (3) in e04rpf, i.e.,

\sum_{i,j = 1}^{n} x_{i} x_{j} Q_{i j}^{k} + \sum_{i = 1}^{n} x_{i} A_{i}^{k} - A_{0}^{k} ⪰ 0, k = 1, \dots, m_{A} .

Therefore the first constraint is defined by matrices

A_{0}^{1} = (\begin{matrix} - 1 & 1 & 0 \\ - 3 / 4 & 0 \\ - 16 \end{matrix}), A_{1}^{1} = (\begin{matrix} 0 & 1 & 0 \\ 0 & 0 \\ 0 \end{matrix}), A_{2}^{1} = (\begin{matrix} 0 & 0 & 1 \\ 0 & 0 \\ 0 \end{matrix})

and the second one by

A_{0}^{2} = (\begin{matrix} 0 & 0 \\ - 1 \end{matrix}), A_{1}^{2} = (\begin{matrix} 1 & 0 \\ 0 \end{matrix}), A_{2}^{2} ​ empty, Q_{12}^{2} = (\begin{matrix} 0 & - 1 \\ 0 & 0 \end{matrix}) .

See also Section 10 in e04raf for links to further examples in the suite.

NAG Library Routine Document

e04ryf (handle_print)

▸▿ Contents

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

6

Error Indicators and Warnings

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

10.2

Program Data

10.3

Program Results

NAG Library Routine Document

e04ryf (handle_print)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results