nag_opt_handle_set_linconstr (e04rjc) (PDF version)
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e04 Chapter Introduction
NAG Library Manual

NAG Library Function Document

nag_opt_handle_set_linconstr (e04rjc)


    1  Purpose
    7  Accuracy

1  Purpose

nag_opt_handle_set_linconstr (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>
#include <nage04.h>
void  nag_opt_handle_set_linconstr (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)

3  Description

After the initialization function nag_opt_handle_init (e04rac) has been called, nag_opt_handle_set_linconstr (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 quadratic programming (QP)
minimize xn 12 xTHx + cTx   (a) subject to   lBBxuB   (b) lxxux ,   (c) (1)
nonlinear programming (NLP)
minimize xn fx   (a) subject to lggxug   (b) lBBxuB   (c) lxxux   (d) (2)
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) (3)
or semidefinite programming with bilinear matrix inequalities (BMI-SDP)
minimize xn 12 xTHx + cTx   (a) subject to   i,j=1 n xi xj Qijk + 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 of the solvers in the suite, nag_opt_handle_solve_ipopt (e04stc) and nag_opt_handle_solve_pennon (e04svc). 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 nag_opt_handle_init (e04rac) for more details.

4  References


5  Arguments

1:     handle void *Input
On entry: the handle to the problem. It needs to be initialized by nag_opt_handle_init (e04rac) and must not be changed.
2:     nclin IntegerInput
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 doubleInput
4:     bu[nclin] const doubleInput
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 IntegerInput
On entry: nnzb gives the number of nonzeros in matrix B.
Constraint: if nclin>0, nnzb>0.
6:     irowb[nnzb] const IntegerInput
7:     icolb[nnzb] const IntegerInput
8:     b[nnzb] const doubleInput
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 nag_opt_handle_init (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 C 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 2.7 in How to Use the NAG Library and its Documentation).

6  Error Indicators and Warnings

Dynamic memory allocation failed.
See Section in How to Use the NAG Library and its Documentation 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 nag_opt_handle_init (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.
An unexpected error has been triggered by this function. Please contact NAG.
See Section 2.7.6 in How to Use the NAG Library and its Documentation 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 2.7.5 in How to Use the NAG Library and its Documentation 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

nag_opt_handle_set_linconstr (e04rjc) is not threaded in any implementation.

9  Further Comments


10  Example

This example demonstrates how to use the MPS file reader nag_opt_miqp_mps_read (e04mxc) and this suite of functions to define and solve a QP problem. nag_opt_miqp_mps_read (e04mxc) uses a different output format to the one required by nag_opt_handle_set_linconstr (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 nag_opt_handle_set_linconstr (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 nag_opt_handle_init (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)

nag_opt_handle_set_linconstr (e04rjc) (PDF version)
e04 Chapter Contents
e04 Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2016