What is the optimal value of a quadratic program when there does not exist a solution?

by jaja   Last Updated April 22, 2018 22:20 PM

If I have a quadratic like so:

$min \frac{1}{2}x^TQx-<b,x>$

and there does not exist a solution, then what is the optimal value?

My intuition tells me that it is negative infinity! beause that's what would happen if the $Q$ matrix were indefinite. But I cannot prove it to myself, even though intuitively this makes sense to me. How would one go about proving that the optimal value must be $-\infty$?

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