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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