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linear_programming (681B)


      1 # Linear programming
      2 
      3 minimize c^t x st A^t x = b and x >= 0 pointwise
      4 - [dual] problem: [variable]s y dans R^d, cost b, we want to minimize b^t y
      5   - and A y \geq c, defines a [polytope]
      6     - so we want to find the point inside the polytope which minimizes the cost
      7 
      8 [algorithm]s (cf [aaron_sidford_talk]):
      9 - [simplex_algorithm], fast in practice but slow in memory
     10 - [ellipsoid], moderate in both
     11 - [interior_point] methods, it's the best in practice
     12 - can be approximated ("first order methods")
     13 - recent improvements
     14 
     15 Up: [optimization]
     16 
     17 See also: [integer_linear_programming], [linear_equation], [linear_relaxation], [farkas_lemma], [linear_algebra_program], [linear_system]