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Is there a way to write a quadratic programming problem with

  1. two variables
  2. bounded, nonempty feasible region
  3. linear constraints

and yet have none of the vertices of the region optimize the objective function?

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consider the squared distance from a point in a square on a plane to a point slightly above the center of the square? (above in the direction orthogonal to the plane) – Steven Stadnicki Sep 29 '12 at 18:35
up vote 3 down vote accepted


max xy

subject to 2x+2y<=10, x,y>=0

The optimal cannot lie on a vertex because then you would be multiplying by 0.

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