# NAG Library Function Document

## 1Purpose

nag_opt_sparse_convex_qp_option_set_file (e04nrc) may be used to supply optional parameters to nag_opt_sparse_convex_qp_solve (e04nqc) from an external file. The initialization function nag_opt_sparse_convex_qp_init (e04npc) must have been called before calling nag_opt_sparse_convex_qp_option_set_file (e04nrc).

## 2Specification

 #include #include
 void nag_opt_sparse_convex_qp_option_set_file (Nag_FileID fileid, Nag_E04State *state, NagError *fail)

## 3Description

nag_opt_sparse_convex_qp_option_set_file (e04nrc) may be used to supply values for optional parameters to nag_opt_sparse_convex_qp_solve (e04nqc). nag_opt_sparse_convex_qp_option_set_file (e04nrc) reads an external file whose fileid has been returned by a call to nag_open_file (x04acc). nag_open_file (x04acc) must be called to provide fileid. Each line of the file defines a single optional parameter. It is only necessary to supply values for those arguments whose values are to be different from their default values.
Each optional parameter is defined by a single character string, consisting of one or more items. The items associated with a given option must be separated by spaces, or equals signs $\left[=\right]$. Alphabetic characters may be upper or lower case. The string
`Print Level = 1`
is an example of a string used to set an optional parameter. For each option the string contains one or more of the following items:
 – a mandatory keyword; – a phrase that qualifies the keyword; – a number that specifies an Integer or double value. Such numbers may be up to $40$ contiguous characters which can be read using C's d or g formats, terminated by a space if this is not the last item on the line.
Blank strings and comments are ignored. A comment begins with an asterisk (*) and all subsequent characters in the string are regarded as part of the comment.
The file containing the options must start with Begin and must finish with End. An example of a valid options file is:
```Begin * Example options file
Print level = 5
End```
Optional parameter settings are preserved following a call to nag_opt_sparse_convex_qp_solve (e04nqc) and so the keyword ${\mathbf{Defaults}}$ is provided to allow you to reset all the optional parameters to their default values before a subsequent call to nag_opt_sparse_convex_qp_solve (e04nqc).
A complete list of optional parameters, their abbreviations, synonyms and default values is given in Section 12 in nag_opt_sparse_convex_qp_solve (e04nqc).

None.

## 5Arguments

1:    $\mathbf{fileid}$Nag_FileIDInput
On entry: the ID of the option file to be read as returned by a call to nag_open_file (x04acc).
2:    $\mathbf{state}$Nag_E04State *Communication Structure
state contains internal information required for functions in this suite. It must not be modified in any way.
3:    $\mathbf{fail}$NagError *Input/Output
The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

## 6Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.
On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.
NE_E04NPC_NOT_INIT
The initialization function nag_opt_sparse_convex_qp_init (e04npc) has not been called.
NE_INTERNAL_ERROR
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 2.7.6 in How to Use the NAG Library and its Documentation for further information.
NE_NO_LICENCE
Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.
At least one line of the options file is invalid.
Could not read options file on unit ${\mathbf{fileid}}=〈\mathit{\text{value}}〉$.
Could not read options file on unit ${\mathbf{fileid}}$. This may be due to:
 (a) ${\mathbf{fileid}}$ is not a valid unit number; (b) a file is not associated with unit ${\mathbf{fileid}}$, or if it is, is unavailable for read access; (c) one or more lines of the options file is invalid. Check that all keywords are neither ambiguous nor misspelt; (d) Begin was found, but end-of-file was found before End was found; (e) end-of-file was found before Begin was found.

Not applicable.

## 8Parallelism and Performance

nag_opt_sparse_convex_qp_option_set_file (e04nrc) is not threaded in any implementation.

nag_opt_sparse_convex_qp_option_set_string (e04nsc), nag_opt_sparse_convex_qp_option_set_integer (e04ntc) or nag_opt_sparse_convex_qp_option_set_double (e04nuc) may also be used to supply optional parameters to nag_opt_sparse_convex_qp_solve (e04nqc).

## 10Example

This example minimizes the quadratic function $f\left(x\right)={c}^{\mathrm{T}}x+\frac{1}{2}{x}^{\mathrm{T}}Hx$, where
 $c = -200.0,-2000.0,-2000.0,-2000.0,-2000.0,400.0,400.0T$
and
 $H= 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 2 0 0 0 0 0 2 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 2 0 0 0 0 0 2 2$
subject to the bounds
 $000≤x1≤0200 000≤x2≤2500 400≤x3≤0800 100≤x4≤0700 000≤x5≤1500 000≤x6≤1500 000≤x7≤1500$
and to the linear constraints
 $x1 + x2 + x3 + x4 + x5 + x6 + x7 = 2000 0.15x1 + 0.04x2 + 0.02x3 + 0.04x4 + 0.02x5 + 0.01x6 + 0.03x7 ≤ 60 0.03x1 + 0.05x2 + 0.08x3 + 0.02x4 + 0.06x5 + 0.01x6 ≤ 100 0.02x1 + 0.04x2 + 0.01x3 + 0.02x4 + 0.02x5 ≤ 40 0.02x1 + 0.03x2 + 0.01x5 ≤ 30 1500 ≤ 0.70x1 + 0.75x2 + 0.80x3 + 0.75x4 + 0.80x5 + 0.97x6 250 ≤ 0.02x1 + 0.06x2 + 0.08x3 + 0.12x4 + 0.02x5 + 0.01x6 + 0.97x7 ≤ 300$
The initial point, which is infeasible, is
 $x0=0.0,0.0,0.0,0.0,0.0,0.0,0.0T.$
The optimal solution (to five figures) is
 $x*=0.0,349.40,648.85,172.85,407.52,271.36,150.02T.$
One bound constraint and four linear constraints are active at the solution. Note that the Hessian matrix $H$ is positive semidefinite.

### 10.1Program Text

Program Text (e04nrce.c)

### 10.2Program Data

Program Options (e04nrce.opt)

Program Data (e04nrce.d)

### 10.3Program Results

Program Results (e04nrce.r)

© The Numerical Algorithms Group Ltd, Oxford, UK. 2017