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The following MPS format input defines a linear programming problem with size constraints and nine variables which are bounded between 0 and 1. The objective function is the sum of the variables. The constraint names node_0, node_1, ..., node_5 are not necessary to describe the problem, but they help to document the formulation and they are useful in viewing dual solutions (if no constraint names are specified, the QSopt parser will assign default names).

Problem      Example01 
Minimize     x0_1 + x0_2 + x0_4 + x1_2 + x1_5 + x2_3 + x3_4 + x3_5 + x4_5
Subject To   node_0: x0_1 + x0_2 + x0_4 = 2 
node_1: x0_1 + x1_2 + x1_5 = 2
node_2: x0_2 + x1_2 + x2_3 = 2   
node_3: x2_3 + x3_4 + x3_5 = 2
node_4: x0_4 + x3_4 + x4_5 = 2   
node_5: x1_5 + x3_5 + x4_5 = 2
Bounds       x0_1 <= 1   x0_2 <= 1   x0_4 <= 1
x1_2 <= 1   x1_5 <= 1   x2_3 <= 1  
x3_4 <= 1   x3_5 <= 1   x4_5 <= 1
End

The following defines the same problem in MPS format.

NAME    Example01
OBJSENSE
MIN
OBJNAME
obj
ROWS
N  obj
E  node_0
E  node_1
E  node_2
E  node_3
E  node_4
E  node_5
COLUMNS
x0_1    obj    1     node_1    1     node_0    1
x0_2    obj    1     node_2    1     node_0    1
x0_4    obj    1     node_4    1     node_0    1
x1_2    obj    1     node_2    1     node_1    1
x1_5    obj    1     node_5    1     node_1    1
x2_3    obj    1     node_3    1     node_2    1
x3_4    obj    1     node_4    1     node_3    1
x3_5    obj    1     node_5    1     node_3    1
x4_5    obj    1     node_5    1     node_4    1
RHS
RHS    node_0    2    node_1    2
RHS    node_2    2    node_3    2
RHS    node_4    2    node_5    2
BOUNDS
UP BOUND    x0_1    1
UP BOUND    x0_2    1
UP BOUND    x0_4    1
UP BOUND    x1_2    1
UP BOUND    x1_5    1
UP BOUND    x2_3    1
UP BOUND    x3_4    1
UP BOUND    x3_5    1
UP BOUND    x4_5    1
ENDATA
 
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Last Updated: November 2003