e04ryc (handle_print) : NAG Library CL Interface, Mark 27

e04ryc 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.

The function may be called by the names: e04ryc or nag_opt_handle_print.

e04ryc prints information on a problem handle which has been previously initialized by e04rac. Various pieces of information can be retrieved and printed to the given output unit. This can be helpful when the function 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 $fail . code =$ NE_ALREADY_DEFINED or NE_PHASE is obtained from functions, such as, e04rec, e04rfc, e04rhc and e04rjc.
Objective: Prints the objective function as it was defined by e04rec or e04rfc if it is linear or quadratic. Prints the sparsity structure of the objective function as it was defined by e04rgc if it is nonlinear or nonlinear least squares by e04rmc.
Simple bounds: Prints the variable bounds as defined by e04rhc. 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 e04rjc.
Cone constraints
Cone constraints detailed: Print all second-order cone constraints as defined by e04rbc. For each constraint print its idgroup, dimension and type. If details are requested, the variables composing the cone constraint are listed as well.
Matrix constraints: Gives a list of the matrix constraints as defined by e04rnc and e04rpc. 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 e04rnc and e04rpc.
Nonlinear constraints bounds
Nonlinear constraints detailed: Print bounds or sparsity structure of the nonlinear constraints as defined by e04rkc.
Multipliers sizes: Prints the expected dimensions of arrays storing the Lagrangian multipliers, such as u and ua of the solver e04svc 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 e04rpc).

See Section 4.1 in the E04 Chapter Introduction for more details about the NAG optimization modelling suite.

On entry: the handle to the problem. It needs to be initialized by e04rac and must not be changed.

On entry: the identifier associated with the file (or standard output) to be written to, as returned by a call of x04acc.

Constraint:

fileid \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.

The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.

On entry, argument

〈value〉

had an illegal value.

On entry,

fileid = 〈value〉

.
Constraint:

fileid \geq 0

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 e04rac or it has been corrupted.

An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.

Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.

cmdstr does not contain any keywords or is empty.

Keyword number

〈value〉

is not recognized.

Keyword number

〈value〉

is not recognized, it is too long.

An error occurred when writing to output.

e04ryc 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 e04rac and e04rpc 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 e04rpc, 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 e04rac for links to further examples in the suite.

NAG CL Interface
e04ryc (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 CL Interfacee04ryc (handle_​print)