ieq(1)                                                     ieq(1)


FORMAT OF '.ieq' - FILES
The first line contains the dimension of the problem.
               DIM = n

In general, lines consisting of a capitalized keyword are signif-
       icant
       for  input recognition. Such keywords can be

               COMMENT
               INEQUALITIES_SECTION
               END

and function specific keywords (such as ELIMINATION_ORDER).
       There is no restriction concerning the order of  sections.
       The keyword

               COMMENT

causes the programs to ignore the text until the next capitalized
       keyword occurs.  The list of equalities resp. inequalities
       starts with the keyword

            INEQUALITIES_SECTION

Each  equation resp. inequalitiy  requires one line. Line numbers
       in  parantheses  are  optional. The  values  are  rational
       and   have to be given by numerator and (optional) denomi-
       nator:

       (ln) num1/den1 xind1 + num2/den2 xind2  .... <= (=>,==)
       numrhs/denrhs

       e.g.: (2) -x2+3/4x5-3x7 >= 4/5
             2x2-  x3 = 8

The keyword
                END

is required to end the file.
       file 'example.ieq':
       DIM = 5

       VALID
       3 3 0 2 3

       LOWER_BOUNDS
       0 1 2 2 2
       UPPER_BOUNDS
       2 2 2 5 5

       ELIMINATION_ORDER
       2 0 1 0 3

       INEQUALITIES_SECTION



                        February 16, 1994                       1





ieq(1)                                                     ieq(1)


       (  1) +27x1-28x2+57x4-37x5 == 0
       (  2)           -  x4+  x5 == 1

       (  1) + x2   -2x5 <=  -3
       (  2)     -x3     <=   0
       -2x2   + x5 <=   0
       -4/15x2-1/15x5 >=  -1

       END
















































                        February 16, 1994                       2