NAG FL Interface
e04rjf (handle_​set_​linconstr)

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1 Purpose

e04rjf is a part of the NAG optimization modelling suite and adds a new block of linear constraints to the problem or modifies an individual linear constraint.

2 Specification

Fortran Interface
Subroutine e04rjf ( handle, nclin, bl, bu, nnzb, irowb, icolb, b, idlc, ifail)
Integer, Intent (In) :: nclin, nnzb, irowb(nnzb), icolb(nnzb)
Integer, Intent (Inout) :: idlc, ifail
Real (Kind=nag_wp), Intent (In) :: bl(nclin), bu(nclin), b(nnzb)
Type (c_ptr), Intent (In) :: handle
C Header Interface
#include <nag.h>
void  e04rjf_ (void **handle, const Integer *nclin, const double bl[], const double bu[], const Integer *nnzb, const Integer irowb[], const Integer icolb[], const double b[], Integer *idlc, Integer *ifail)
The routine may be called by the names e04rjf or nagf_opt_handle_set_linconstr.

3 Description

After the handle has been initialized (e.g., e04raf has been called), e04rjf may be used to add to the problem a new block of mB linear constraints
where B is a general mB×n rectangular matrix, n is the current number of decision variables in the model and lB and uB are mB-dimensional vectors defining the lower and upper bounds, respectively. The call can be repeated to add multiple blocks to the model.
Note that the bounds are specified for all the constraints of this block. 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 routine and any later alterations to Infinite Bound Size will not affect these constraints.
The linear constraints can be edited. To identify the individual constraints, they are numbered starting with 1, see idlc. A single constraint (i.e., a single row of the matrix B) can be modified (replaced) by e04rjf by referring to its idlc. An individual coefficient bij of the matrix B can be set or modified by e04tjf and bounds of a single constraint can be set or modified by e04tdf. Note that it is also possible to temporarily disable and enable individual constraints in the model by e04tcf and e04tbf, respectively.
Linear constraints may be present in many different types of problems, for simplicity of the notation, only one block of linear constraints is presented. For example,
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)
Quadratically Constrained Quadratic Programming (QCQP)
minimize xn 12 xTHx + cTx   (a) subject to   12 xTQkx + rkTx + sk0 ,  k=1,,mQ ,   (b) lBBxuB,   (c) lxxux ,   (d) (3)
Nonlinear Programming (NLP)
minimize xn f(x)   (a) subject to lgg(x)ug,   (b) 12 xTQkx + rkTx + sk0 ,  k=1,,mQ ,   (c) lBBxuB,   (d) lxxux,   (e) (4)
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) (5)
See Section 3.1 in the E04 Chapter Introduction for more details about the NAG optimization modelling suite.

4 References


5 Arguments

1: handle Type (c_ptr) Input
On entry: the handle to the problem. It needs to be initialized (e.g., by e04raf) and must not be changed between calls to the NAG optimization modelling suite.
2: nclin Integer Input
On entry: mB, the number of linear constraints (number of rows of the matrix B) in this block.
If nclin=0, no linear constraints will be added and bl, bu, nnzb, irowb, icolb and b will not be referenced.
  • nclin0;
  • if idlc>0, nclin=1.
3: bl(nclin) Real (Kind=nag_wp) array Input
4: bu(nclin) Real (Kind=nag_wp) array 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)=bu(j)=β, where |β|<bigbnd. To specify a nonexistent lower bound (i.e., lj=-), set bl(j)-bigbnd; to specify a nonexistent upper bound, set bu(j)bigbnd.
  • bl(j)bu(j), for j=1,2,,nclin;
  • bl(j)<bigbnd, for j=1,2,,nclin;
  • bu(j)>-bigbnd, for j=1,2,,nclin;
  • if bl(j)=bu(j), |bl(j)|<bigbnd, for j=1,2,,nclin.
5: nnzb Integer Input
On entry: nnzb gives the number of nonzeros in matrix B.
Constraint: nnzb0.
6: irowb(nnzb) Integer array Input
7: icolb(nnzb) Integer array Input
8: b(nnzb) Real (Kind=nag_wp) array 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 is the current number of decision variables in the model. 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) where i=irowb(l) and j=icolb(l), for l=1,2,,nnzb. No particular order of elements is expected, but elements should not repeat.
Constraint: 1irowb(l)nclin, 1icolb(l)n, for l=1,2,,nnzb.
9: idlc Integer Input/Output
On entry: if idlc=0, a new block of linear constraints is added to the model; otherwise, idlc>0 refers to the number of an existing linear constraint which will be replaced and nclin must be set to one.
Constraint: idlc0.
On exit: if idlc=0, the number of the last linear constraint added. By definition, it is the number of linear constraints already defined plus nclin. Otherwise, idlc>0 stays unchanged.
10: ifail Integer Input/Output
On entry: ifail must be set to 0, −1 or 1 to set behaviour on detection of an error; these values have no effect when no error is detected.
A value of 0 causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of −1 means that an error message is printed while a value of 1 means that it is not.
If halting is not appropriate, the value −1 or 1 is recommended. If message printing is undesirable, then the value 1 is recommended. Otherwise, the value −1 is recommended. When the value -1 or 1 is used it is essential to test the value of ifail on exit.
On exit: ifail=0 unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

If on entry ifail=0 or −1, explanatory error messages are output on the current error message unit (as defined by x04aaf).
Errors or warnings detected by the routine:
The supplied handle does not define a valid handle to the data structure for the NAG optimization modelling suite. It has not been properly initialized or it has been corrupted.
The problem cannot be modified right now, the solver is running.
On entry, idlc=value.
Constraint: idlc0.
On entry, idlc=value.
The given idlc does not match with any existing linear constraint.
The maximum idlc is value.
On entry, idlc=value and nclin=value.
Constraint: If idlc>0, nclin=1.
On entry, nclin=value.
Constraint: nclin0.
On entry, nnzb=value.
Constraint: nnzb0.
On entry, i=value, icolb(i)=value and n=value.
Constraint: 1icolb(i)n.
On entry, i=value, irowb(i)=value and nclin=value.
Constraint: 1irowb(i)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.
On entry, j=value, bl(j)=value, bigbnd=value.
Constraint: bl(j)<bigbnd.
On entry, j=value, bl(j)=value and bu(j)=value.
Constraint: bl(j)bu(j).
On entry, j=value, bu(j)=value, bigbnd=value.
Constraint: bu(j)>-bigbnd.
An unexpected error has been triggered by this routine. Please contact NAG.
See Section 7 in the Introduction to the NAG Library FL 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 FL Interface for further information.
Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

Not applicable.

8 Parallelism and Performance

e04rjf is not threaded in any implementation.

9 Further Comments

9.1 Internal Changes

Internal changes have been made to this routine as follows:
For details of all known issues which have been reported for the NAG Library please refer to the Known Issues.

10 Example

This example demonstrates how to use the MPS file reader e04mxf and this suite of routines to define and solve a QP problem. e04mxf uses a different output format to the one required by e04rjf, 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 e04rjf 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 e04raf for links to further examples in this suite.

10.1 Program Text

Program Text (e04rjfe.f90)

10.2 Program Data

Program Options (e04rjfe.opt)

10.3 Program Results

Program Results (e04rjfe.r)