LinearProgramming
 Usage
Notes
 Further Examples
This solves an equality-constrained problem. The expression  is minimized subject to  . The zero indicates equality.
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This solves a problem with no constraints other than bounds. The expression  is minimized subject to    and      .
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This solves a problem with only lower bounds. The expression  is minimized subject to    and    .
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This solves a problem with no bounds on the second variable. The expression  is minimized subject to    and    . The number  indicates " ".
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This solves a problem with the second variable fixed to be  . The expression  is minimized subject to    ,    and  .
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The above problem can also be solved by writing the fixed variable  as the equality constraint,  and setting its bounds to any that catch the value  , such as  .
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This solves a problem with both equality and inequality constraints as well as bounds. The expression  is minimized subject to    ,  ,      and      .
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The Klee-Minty problem of dimension  is
Maximize 10000 y[1] + 1000 y[2] + 100 y[3] + 10 y[4] + y[5]
subject to y[1]  1,
20 y[1] + y[2]  100,
200 y[1] + 20 y[2] + y[3]  
2000 y[1] + 200 y[2] + 20 y[3] + y[4]  
20000 y[1] + 2000 y[2] + 200 y[3] + 20 y[4] + y[5]  
y[1]  0, y[2]  0, y[3]  0, y[4]  0, y[5]  0.
This expresses the Klee-Minty problem of dimension  in the LinearProgramming syntax.
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Without scaling, the simplex algorithm takes an exponential number of iterations to converge. Evaluate the previous cell to define KleeMinty.
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With scaling, which is applied by default, the simplex algorithm converges very quickly.
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