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