NAG Toolbox: nag_mip_ilp_info (h02bz)

Purpose

Syntax

Description

References

Parameters

Compulsory Input Parameters

1:     $\mathrm{n}$ – int64int32nag_int scalar

This must be the same argument n as supplied to nag_mip_ilp_dense (h02bb).

Constraint: $\mathbf{n}>0$.

2:     $\mathrm{m}$ – int64int32nag_int scalar

This must be the same argument m as supplied to nag_mip_ilp_dense (h02bb).

Constraint: $\mathbf{m}\ge 0$.

3:     $\mathrm{iwork}\left(\mathit{liwork}\right)$ – int64int32nag_int array

This must be the same argument iwork as supplied to nag_mip_ilp_dense (h02bb). It is used to pass information from nag_mip_ilp_dense (h02bb) to nag_mip_ilp_info (h02bz) and therefore the contents of this array must not be changed before calling nag_mip_ilp_info (h02bz).

4:     $\mathrm{rwork}\left(\mathit{lrwork}\right)$ – double array

This must be the same argument rwork as supplied to nag_mip_ilp_dense (h02bb). It is used to pass information from nag_mip_ilp_dense (h02bb) to nag_mip_ilp_info (h02bz) and therefore the contents of this array must not be changed before calling nag_mip_ilp_info (h02bz).

Optional Input Parameters

None.

Output Parameters

1:     $\mathrm{bl}\left(\mathbf{n}+\mathbf{m}\right)$ – double array

If nag_mip_ilp_dense (h02bb) exits with $\mathbf{ifail}=\mathbf{0}$, $\mathbf{7}$ or $\mathbf{9}$, the values in the array bl contain the lower bounds imposed on the integer solution for all the constraints. The first n elements contain the lower bounds on the variables, and the next m elements contain the lower bounds for the general linear constraints (if any).

2:     $\mathrm{bu}\left(\mathbf{n}+\mathbf{m}\right)$ – double array

If nag_mip_ilp_dense (h02bb) exits with $\mathbf{ifail}=\mathbf{0}$, $\mathbf{7}$ or $\mathbf{9}$, the values in the array bu contain the upper bounds imposed on the integer solution for all the constraints. The first n elements contain the upper bounds on the variables, and the next m elements contain the upper bounds for the general linear constraints (if any).

3:     $\mathrm{clamda}\left(\mathbf{n}+\mathbf{m}\right)$ – double array

If nag_mip_ilp_dense (h02bb) exits with $\mathbf{ifail}=\mathbf{0}$, $\mathbf{7}$ or $\mathbf{9}$, the values in the array clamda contain the values of the Lagrange-multipliers for each constraint with respect to the current working set. The first n elements contain the multipliers (reduced costs) for the bound constraints on the variables, and the next m elements contain the multipliers (shadow costs) for the general linear constraints (if any).

4:     $\mathrm{istate}\left(\mathbf{n}+\mathbf{m}\right)$ – int64int32nag_int array

If nag_mip_ilp_dense (h02bb) exits with $\mathbf{ifail}=\mathbf{0}$, $\mathbf{7}$ or $\mathbf{9}$, the values in the array istate indicate the status of the constraints in the working set at an integer solution. Otherwise, istate indicates the composition of the working set at the final iterate. The significance of each possible value of $\mathbf{istate}\left(j\right)$ is as follows.

$\mathbf{istate}\left(j\right)$	Meaning
$-2$	The constraint violates its lower bound by more than tolfes (the feasibility tolerance, see nag_mip_ilp_dense (h02bb)).
$-1$	The constraint violates its upper bound by more than tolfes.
$\phantom{-}0$	The constraint is satisfied to within tolfes, but is not in the working set.
$\phantom{-}1$	This inequality constraint is included in the working set at its lower bound.
$\phantom{-}2$	This inequality constraint is included in the working set at its upper bound.
$\phantom{-}3$	This constraint is included in the working set as an equality. This value of istate can occur only when $\mathbf{bl}\left(j\right)=\mathbf{bu}\left(j\right)$.
$\phantom{-}4$	This corresponds to an integer solution being declared with $x_j$ being temporarily fixed at its current value. This value of istate can occur only when $\mathbf{ifail}=\mathbf{0}$, $\mathbf{7}$ or $\mathbf{9}$ on exit from nag_mip_ilp_dense (h02bb).

5:     $\mathrm{ifail}$ – int64int32nag_int scalar

$\mathbf{ifail}=\mathbf{0}$ unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

   $\mathbf{ifail}=1$

On entry,	$\mathbf{n}\le 0$,
or	$\mathbf{m}<0$.

   $\mathbf{ifail}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

   $\mathbf{ifail}=-399$

Your licence key may have expired or may not have been installed correctly.

   $\mathbf{ifail}=-999$

Dynamic memory allocation failed.

Accuracy

Further Comments

Example

Open in the MATLAB editor: h02bz_example

function h02bz_example


fprintf('h02bz example results\n\n');

% Find vector x of length n that Minimizes c.x subject to:
% bl(1:n) <= x <= bu(1:n) and m linear contraints
% bl(n+1:n+m) <= Ax <= bu(n+1:n_m)
n = int64(6);
m = int64(3);
a  = [110,  205,   160,   160,   420,   260;
        4,   32,    13,     8,     4,    14;
        2,   12,    54,   285,    22,    80];
bl = [  0;    0;     0;     0;     0;     0;   2000;     55;     800];
bu = [  4;    3;     2;     8;     2;     2;  1e+20;  1e+20;   1e+20];

% All of x is integer.
intvar = int64([1;  1;  1;  1;  1;  1]);
c      =         [3; 24; 13;  9; 20; 19];
% Initial guess
x      = zeros(6,1);

itmax  = int64(0);
msglvl = int64(0);
maxnod = int64(0);
intfst = int64(0);
toliv  = 0;
tolfes = 0;
bigbnd = 1e+20;
[itmax, toliv, tolfes, bigbnd, x, objmip, iwork, rwork, ifail] = ...
h02bb( ...
       itmax, msglvl, a, bl, bu, intvar, c, maxnod, ...
       intfst, toliv, tolfes, bigbnd, x);

% Extract further solution information and display
[bl, bu, clamda, istate, ifail] = ...
h02bz(n, m, iwork, rwork);

fprintf('Final IP objective value = %11.4f\n\n',objmip)

fprintf('%6s%8s%8s%16s%14s%13s\n','Varbl','State','Value',...
        'Lower Bound','Upper Bound','Lagr Mult');

chstate = ['VL';'VU';'FR';'LL';'UU';'EQ';'TF'];
vch = ['Oatmeal';'Chicken';'Eggs   ';'Milk   ';'Pie    ';'Bacon  '];
cch = ['Energy ';'Protein';'Calcium'];

for i=1:n
  ich = double(istate(i)) + 3;
  fprintf('%7s%6s%10.2f%14.2f%14.2f%13.2f\n',vch(i,:),...
          chstate(ich,:),x(i),bl(i),bu(i),clamda(i))
end

fprintf('\n%6s%8s%8s%16s%14s%13s\n','L Con','State','Value',...
        'Lower Bound','Upper Bound','Lagr Mult');
y = a*x;
for i=n+1:n+m
  ich = double(istate(i)) + 3;
  fprintf('%7s%6s%10.2f%14.2f%14.2e%13.2f\n',cch(i-n,:),...
          chstate(ich,:),y(i-n),bl(i),bu(i),clamda(i))
end

h02bz example results

Final IP objective value =     97.0000

 Varbl   State   Value     Lower Bound   Upper Bound    Lagr Mult
Oatmeal    EQ      4.00          4.00          4.00         3.00
Chicken    LL      0.00          0.00          3.00        24.00
Eggs       LL      0.00          0.00          2.00        13.00
Milk       LL      5.00          5.00          8.00         9.00
Pie        EQ      2.00          2.00          2.00        20.00
Bacon      LL      0.00          0.00          2.00        19.00

 L Con   State   Value     Lower Bound   Upper Bound    Lagr Mult
Energy     FR   2080.00       2000.00      1.00e+20         0.00
Protein    FR     64.00         55.00      1.00e+20         0.00
Calcium    FR   1477.00        800.00      1.00e+20         0.00