I have the following constraint $$ x^TAx+b^Tx=c $$ where $A$ is a positive definite matrix. Is there any way to take advantage of the strict convexity of this expression to reformulate the constraint as something simpler?
Thoughts/attempt:
I was thinking we could form $$B = A^{1/2}$$ and maybe introduce a change-of-variable as a start, but I'm not sure if this leads anywhere.