Example of a quadratic programming problem with no optimal solution on vertices?

Question

Is there a way to write a quadratic programming problem with

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

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)

Takkun · Accepted Answer · 2012-09-29 23:15:09Z

up vote 3 down vote accepted

Answer:

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.

answered Sep 29 '12 at 23:15

Takkun
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1 Answer