e04raf initializes an empty problem with
$n$ decision variables,
$x$, and returns a handle to the data structure. This handle may then be passed to some of the routines
e04rbf,
e04ref,
e04rff,
e04rgf,
e04rhf,
e04rjf,
e04rkf,
e04rlf,
e04rmf,
e04rnf and
e04rpf to formulate the problem (define the objective function and constraints) and to a compatible solver,
e04fff,
e04fgf,
e04jdf,
e04jef,
e04kff,
e04mtf,
e04ptf,
e04stf or
e04svf, to solve it. The handle
must not be changed between calls. 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
$1$, explanatory error messages are output on the current error message unit (as defined by
x04aaf).
Not applicable.
None.
See examples associated with other routines in the suite, such as:

–the examples in Section 10 in e04fff and Section 10 in e04fgf present a data fitting problem solved by a DFO LSQ solver,

–the examples in Section 10 in e04jdf and Section 10 in e04jef demonstrate how to use a DFO NLP solver,

–the example in Section 10 in e04kff solves a boxconstrained nonlinear problem with a firstorder solver,

–the example in Section 10 in e04mtf solves a small LP example using an LP IPM solver,

–the example in Section 10 in e04ptf solves a small convex QCQP problem reformulated as SOCP,

–the example in Section 10 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 Section 10 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 Section 10 in e04rhf, the example also demonstrates the monitoring mode of the solver e04svf,

–the example in Section 10 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 Section 10 in e04rnf,

–the example in Section 10 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 example in Section 10 in e04rxf demonstrates how an approximate solution can be extracted during a monitoring step of e04mtf,

–the example in Section 10 in e04ryf walks through the life cycle of the handle in which a BMISDP problem is formulated and solved,

–an example in Section 10 in e04stf is a small test from Hock and Schittkowski set to show how to call the NLP solver,

–the simple example in Section 10 in e04svf demonstrates on the Lovász $\vartheta $ function eigenvalue optimization problem formulated as SDP.