e04raf initializes an empty problem, adds
$n\ge 0$ decision variables,
$x$, and returns a handle to the data structure. Note that further variables may be added to the problem later by
e04taf and it is also possible to temporarily disable and enable individual variables in the model by
e04tcf and
e04tbf, respectively. This handle may then be passed to some of the routines of the suite to formulate the problem (define or edit the variables, the objective function and constraints). Once the problem is fully defined, the handle may be passed to a suitable solver from the suite (
e04fff,
e04fgf,
e04ggf,
e04jdf,
e04jef,
e04kff,
e04mtf,
e04ptf,
e04stf or
e04svf). Afterwards, the problem may be further modified or passed to another solver of the suite. The handle
must not be changed between calls to the routines of the suite. When the handle is no longer needed,
e04rzf must be called to destroy it and deallocate all the allocated memory and data within. See
Section 3.1 in the
E04 Chapter Introduction for more details about the NAG optimization modelling suite.
None.
If on entry
${\mathbf{ifail}}=0$ or
$\mathrm{1}$, explanatory error messages are output on the current error message unit (as defined by
x04aaf).
Not applicable.
Background information to multithreading can be found in the
Multithreading documentation.
None.
See examples associated with other routines in the suite, such as:

–the examples in e04fff and e04fgf present a data fitting problem solved by a DFO LSQ solver,

–the example in e04ggf solves a nonlinear regression (data fitting) problem with a trustregion based nonlinear least squares solver,

–the examples in e04jdf and e04jef demonstrate how to use a DFO NLP solver,

–the example in e04kff solves a boxconstrained nonlinear problem with a firstorder solver,

–the example in e04mtf solves a small LP example using an LP IPM solver,

–the example in e04ptf solves a small Secondorder Cone Programming (SOCP) problem,

–the example in e04rdf demonstrates how to use the SDPA file reader and how to solve linear semidefinite programming problems, including printing of the matrix Lagrangian multipliers,

–the example in e04rff presents an alternative way to compute the nearest correlation matrix by means of nonlinear semidefinite programming,

–a matrix completion problem (minimization of a rank of a partially unknown matrix) formulated as SDP is demonstrated in e04rhf, the example also demonstrates the monitoring mode of the solver e04svf,

–the example in e04rjf solves LP/QP problems read in from an MPS file by e04mxf,

–an application for statistics, $E$ optimal design, solved as an SDP problem is shown in e04rnf,

–the example in e04rpf reads a BMISDP problem from a file which can be modified, in this case it solves a Static Output Feedback (SOF) problem,

–the examples in e04rsf and e04rtf solve small convex QCQP problems which are automatically reformulated as SOCP,

–the example in e04rxf demonstrates how an approximate solution can be extracted during a monitoring step of e04mtf,

–the example in e04ryf walks through the life cycle of the handle in which a BMISDP problem is formulated and solved,

–the example in e04saf might serve as a template for benchmarking when a problem is loaded from a file and passed directly to the solver, in this case e04ptf,

–the example in e04stf is a small test from Hock and Schittkowski set to show how to call the NLP solver,

–the simple example in e04svf demonstrates on the Lovász $\vartheta $ function eigenvalue optimization problem formulated as SDP,

–modelling capabilities of the suite (edits of an existing problem) are demonstrated in the examples in e04taf and e04tcf.