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Strong Duality Theorem in Linear Programming

  1. Feb 12, 2012 #1
    If a linear Program (P) has a feasible solution [itex]x_{o}[/itex], ( [itex]x_{o}[/itex] not necessarily optimal),does it follow that there exists a feasible solution to the dual problem (D) as well? If yes, why?

    I know that the Strong Duality Theorem guarantees an optimal finite solution to the dual problem if the primal problem has an optimal finite solution. But I cannot see why this would be the case if the feasible solution to the primal is not necessarily optimal.
     
  2. jcsd
  3. Feb 13, 2012 #2

    Ray Vickson

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    If P is the primal and D is the dual, the possibilities are: (i) P and D are both feasible (in which case they both have finite optimal solutions with equal objectives); (ii) P is feasible and D is infeasible (in which case P has no finite optimum); (iii) D is feasible and P is infeasible (in which case D has no finite optimum); (iv) both P and D are infeasible.

    RGV
     
  4. Feb 13, 2012 #3
    Thanks :). That helps!
     
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