Escapable nonlinearities

• Absolute values

  • Introduce auxiliary variables
  • min |x – y| ? min z+ + z-
    s.t. x - y = z+ - z-
    
    z- , z+ >=0
    

• Transformations via monotonic functions

  • E.g., use logarithms
    • y = 3x1+x2 ? log y = (x1+ x2 )(log3)
  • and make substitution of variables
    • Y = log y
      

• Min/max problems

  • Introduce auxiliary variables
  • min { max {x1,x2}} ? min z
    s.t. z >= x1, z >= x2
    

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