NAG CL Interface
e04rjc (handle_​set_​linconstr)

1 Purpose

e04rjc is a part of the NAG optimization modelling suite and defines the block of linear constraints of the problem.

2 Specification

#include <nag.h>
void  e04rjc (void *handle, Integer nclin, const double bl[], const double bu[], Integer nnzb, const Integer irowb[], const Integer icolb[], const double b[], Integer *idlc, NagError *fail)
The function may be called by the names: e04rjc or nag_opt_handle_set_linconstr.

3 Description

After the initialization function e04rac has been called, e04rjc may be used to define the linear constraints lBBxuB of the problem unless the linear constraints have already been defined. This will typically be used for problems, such as linear programming (LP)
minimize xn cTx   (a) subject to   lBBxuB,   (b) lxxux ,   (c) (1)
quadratic programming (QP)
minimize xn 12 xTHx + cTx   (a) subject to   lBBxuB,   (b) lxxux ,   (c) (2)
nonlinear programming (NLP)
minimize xn fx   (a) subject to lggxug,   (b) lBBxuB,   (c) lxxux,   (d) (3)
or linear semidefinite programming (SDP)
minimize xn cTx   (a) subject to   i=1 n xi Aik - A0k 0 ,  k=1,,mA ,   (b) lBBxuB,   (c) lxxux,   (d) (4)
where n is the number of decision variables, B is a general mB×n rectangular matrix and lB and uB are mB-dimensional vectors. Note that upper and lower bounds are specified for all the constraints. This form allows full generality in specifying various types of constraint. In particular, the jth constraint may be defined as an equality by setting lj=uj. If certain bounds are not present, the associated elements of lB or uB may be set to special values that are treated as - or +. See the description of the optional parameter Infinite Bound Size which is common among all solvers in the suite. Its value is denoted as bigbnd further in this text. Note that the bounds are interpreted based on its value at the time of calling this function and any later alterations to Infinite Bound Size will not affect these constraints.
See Section 4.1 in the E04 Chapter Introduction for more details about the NAG optimization modelling suite.

4 References


5 Arguments

1: handle void * Input
On entry: the handle to the problem. It needs to be initialized by e04rac and must not be changed before the call to e04rjc.
2: nclin Integer Input
On entry: mB, the number of linear constraints (number of rows of the matrix B).
If nclin=0, no linear constraints will be defined and bl, bu, nnzb, irowb, icolb and b will not be referenced and may be NULL.
Constraint: nclin0.
3: bl[nclin] const double Input
4: bu[nclin] const double Input
On entry: bl and bu define lower and upper bounds of the linear constraints, lB and uB, respectively. To define the jth constraint as equality, set bl[j-1]=bu[j-1]=β, where β<bigbnd. To specify a nonexistent lower bound (i.e., lj=-), set bl[j-1]-bigbnd; to specify a nonexistent upper bound, set bu[j-1]bigbnd.
  • bl[j-1]bu[j-1], for j=1,2,,nclin;
  • bl[j-1]<bigbnd, for j=1,2,,nclin;
  • bu[j-1]>-bigbnd, for j=1,2,,nclin;
  • if bl[j-1]=bu[j-1], bl[j-1]<bigbnd, for j=1,2,,nclin.
5: nnzb Integer Input
On entry: nnzb gives the number of nonzeros in matrix B.
Constraint: if nclin>0, nnzb>0.
6: irowb[nnzb] const Integer Input
7: icolb[nnzb] const Integer Input
8: b[nnzb] const double Input
On entry: arrays irowb, icolb and b store nnzb nonzeros of the sparse matrix B in coordinate storage (CS) format (see Section 2.1.1 in the F11 Chapter Introduction). The matrix B has dimensions mB×n, where n, the number of variables in the problem, was set in nvar during the initialization of the handle by e04rac. irowb specifies one-based row indices, icolb specifies one-based column indices and b specifies the values of the nonzero elements in such a way that bij=b[l-1] where i=irowb[l-1] and j=icolb[l-1], for l=1,2,,nnzb. No particular order of elements is expected, but elements should not repeat.
Constraint: 1irowb[l-1]nclin, 1icolb[l-1]n, for l=1,2,,nnzb.
9: idlc Integer * Input/Output
Note: idlc is reserved for future releases of the NAG Library.
On entry: if idlc=0, new linear constraints are added to the problem definition. This is the only value allowed at the moment.
Constraint: idlc=0.
On exit: the number of the last linear constraint added, thus nclin.
10: fail NagError * Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
A set of linear constraints has already been defined.
On entry, argument value had an illegal value.
On entry, j=value, bl[j-1]=value, bigbnd=value.
Constraint: bl[j-1]<bigbnd.
On entry, j=value, bl[j-1]=value and bu[j-1]=value.
Constraint: bl[j-1]bu[j-1].
On entry, j=value, bu[j-1]=value, bigbnd=value.
Constraint: bu[j-1]>-bigbnd.
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.
On entry, nclin=value.
Constraint: nclin0.
On entry, nnzb=value.
Constraint: nnzb>0.
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.
On entry, i=value, icolb[i-1]=value and n=value.
Constraint: 1icolb[i-1]n.
On entry, i=value, irowb[i-1]=value and nclin=value.
Constraint: 1irowb[i-1]nclin.
On entry, more than one element of b has row index value and column index value.
Constraint: each element of b must have a unique row and column index.
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.
The problem cannot be modified in this phase any more, the solver has already been called.
On entry, idlc=value.
Constraint: idlc=0.

7 Accuracy

Not applicable.

8 Parallelism and Performance

e04rjc is not threaded in any implementation.

9 Further Comments


10 Example

This example demonstrates how to use the MPS file reader e04mxc and this suite of functions to define and solve a QP problem. e04mxc uses a different output format to the one required by e04rjc, in particular, it uses the compressed column storage (CCS) (see Section 2.1.3 in the F11 Chapter Introduction) instead of the coordinate storage and the linear objective vector is included in the system matrix. Therefore a simple transformation is needed before calling e04rjc as demonstrated in the example program.
The data file stores the following problem:
minimize cT x + 12 xT H x   subject to   lB Bx uB, -2 Ax 2,  
c= -4.0 -1.0 -1.0 -1.0 -1.0 -1.0 -1.0 -0.1 -0.3 ,   H= 2 1 1 1 1 0 0 0 0 1 2 1 1 1 0 0 0 0 1 1 2 1 1 0 0 0 0 1 1 1 2 1 0 0 0 0 1 1 1 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ,  
B= 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 4.0 1.0 2.0 3.0 4.0 -2.0 1.0 1.0 1.0 1.0 1.0 -1.0 1.0 -1.0 1.0 1.0 1.0 1.0 1.0 ,  
lB= -2.0 -2.0 -2.0   and   uB= 1.5 1.5 4.0 .  
The optimal solution (to five figures) is
See also Section 10 in e04rac for links to further examples in this suite.

10.1 Program Text

Program Text (e04rjce.c)

10.2 Program Data

Program Options (e04rjce.opt)

10.3 Program Results

Program Results (e04rjce.r)