IBM QP User Guide

IBM Optimization Solutions and Library QP Solutions User Guide

Name: oslqbslv

Purpose: To solve Quadratic Programming problems using interior point methods
Usage: oslqbslv [?] [-keyword=value] [...] [@keyword_file]
keyword_file: Name of file containing "-keyword=value" strings.
(Each "-keyword=value" string in this file must be on a separate line.)

Valid Keywords and Default Values:

maxmin = min|max - default: min
input = input_mps_file - default: standard input
output = listing_file - default: standard output
dspace = value - default: 400000
isolmask = value - default: 0
iprtinfomask = value - default: 31
scale = yes|no - default: yes
imaxiter = value - default: 9999999
osli_n_ = value - default: a function of n
oslr_n_ = value - default: a function of n
oslc_n_ = value - default: a function of n

See the library User's Guide for more information on Control variables.

Explanation of Keywords:

maxmin : Solve as a maximization or minimization problem.
input : Name of file containing input data - MPS format.
output : Name of file to receive messages.
dspace : Size in double words of the work area.
isolmask : Matrix bit mask for EKKPRTS print function.
= 1 : selects the rows
= 2 : selects the columns
= 4 : selects the nonzero elements of the model
= 8 : selects the infeasible elements of the model
= 15 or 0 or 16 : selects the entire matrix

Iprtinfomask : Solution information bit mask for EKKPRTS print function.

= 1 : selects the statistics
= 2 : selects iteration count, value of the objective function
and the problem status
= 4 : selects the names of the columns and rows
= 8 : selects the status of each variable
= 16 : selects the row and column solution values
= 32 : selects the dual values and reduced costs
= 64 : selects the lower bounds
= 128 : selects the upper bounds
= 256 : selects the input costs
= 512 : selects the matrix elements
= 0 : selects the first six options (i.e., same as 63).
scale : Use EKKSCAL function to scale the coefficient matrix.
imaxiter : The maximum number of iterations that will be performed.
osli_n_ : Integer Control variable n; 0 < n < 62
oslr_n_ : Real Control variable n; 0 < n < 46
oslc_n_ : Character Control variable n; 0 < n < 11

Example 1

oslqbslv ?

This command results in the display of valid keywords, their meanings along with the default values.

Example 2

oslqbslv -imaxiter=20000 < test1.mps > test1.out

The oslqbslv program is started using test1.mps as input data. Output is directed to the file test1.out. The program will stop after 20000 iterations.

Example 3

If the file key_file.001 contains the following 4 lines:

maxmin=max
imaxiter=20000
isolmask=7
osli_36_=132

then the command:

oslqbslv -dspace=1000000 @key_file.001 < test1.mps > test1.out

will start oslqbslv with a work area of 1 million double words. The problem is solved as a maximization problem. The program will stop after 20000 iterations. The ekkprts() print function will select only non-zero columns and rows. The maximum number of characters on each line of output is 132.

Example 4

The command:

oslqbslv -dspace=1000000 @key_file.001 -input=test1.mps -output=test1.out

is equivalent to:

oslqbslv -dspace=1000000 @key_file.001 < test1.mps > test1.out

Example 5

The quadratic part of the objective function of the following problem:

Minimize

x1 + 2.4*x2 - x3 + 1.1*x4
   + (x1*x1 + 2*x2*x2 + 1.5*x3*x3 + x4*x4 + x1*x2 -2*x2*x3)

Subject to:

3*x1 + x2        - 2*x4 >= 2.5
       x2 +   x3 + 4*x4  = 4.0

0 <= x1 <= 3;  x2 <= 2;  x3 >= 0;  x4 >= 0;

can be written as (1/2) x Qx where Q is:

.-          -.
| 2  1  0  0 |
| 1  4 -2  0 |
| 0 -2  3  0 |
| 0  0  0  2 |
.-          -.

The MPS file for this problem is shown below. This example is from the book "Optimization with IBM OSL" by M.S. Hung, W.O. Rom, and A.D. Waren, Boyd and Fraser Publishing Co., 1994 (ISBN 0-89426-244-0). Please note, however, that the optimal solution shown in the output listing on page 310 of this book is incorrect. The output listing shown on pages 309-310 correspond to a different problem.

MPS file for QP1

NAME          QP1
ROWS
 N  OBJ
 G  ROW1
 E  ROW2
COLUMNS
    X1        OBJ              1.0D0   ROW1             3.0D0
    X2        OBJ              2.4D0   ROW1             1.0D0
    X2        ROW2              1.D0
    X3        OBJ              -1.D0   ROW2              1.D0
    X4        OBJ             1.1 D0   ROW1             -2.D0
    X4        ROW2              4.D0
RHS
    BVEC      ROW1             2.5D0   ROW2              4.D0
BOUNDS
 UP BNDU      X1                3.D0
 UP BNDU      X2                2.D0
 LO BNDU      X2              -1.D31
ENDATA
NAME          QP1
QSECTION
    X1        X1                2.D0     X2               1.D0
    X2        X1                1.D0     X2               4.D0
    X2        X3               -2.D0
    X3        X2               -2.D0     X3               3.D0
    X4        X4                2.D0
ENDATA

oslqbslv USAGE NOTES

If oslqbslv is having difficulty with a problem, then you should increase the size of work area, using the "dspace" keyword, and try solving the problem again.
oslqbslv uses the library I/O function ekkmps() to read the linear part of the problem and ekkqmps() to read the quadratic part. The same input file ,is used for both ekkmps() and ekkqmps() so the records for the quadratic data must follow the ENDATA record for the linear components. The Q matrix appears after a QSECTION indicator record, which must be preceded by a NAME indicator record. The format for the Q matrix is similar to that for the usual MPS COLUMNS section. The Q matrix data records must also be followed by an ENDATA record.