How can I find the optimal solution of quadratic function

Question

How can I minimize or maximize a quadratic function? what is the algorithm for that?

Thanks!

It's a more general question but for example, X^TAX where A is a matrix, does is there are constrains the algorithm change? — AdyM, May 29 '21 at 13:27
btw you should ask this question here: https://math.stackexchange.com . — ulou, May 29 '21 at 13:33

score 0 · Answer 1 · answered May 29 '21 at 13:25

If you're talking about polynomials of degree in the form

y = a·x² + b·x + c

There's a very simple, closed solution for that. Take the arithmetic average of the the two roots as given by the general solution

x1,2 = (-b +/- sqrt(b² + 4·a·c)) / 2·a

That gives you the x value for the min or max.

Take the 2nd derivative of the polynomial to see if its a minimum or a maximum.

All of these have simple closed solution, but this reeks of homework, so I want you do to something.

1 Answers1