Consider the problem minimize 5x 2 +5y 2 −xy −11x+11y +11 a) Find a point satisfying the first-order necessary conditions for a solution. b) Show that this point is a global minimum. c) What would be...

Consider the problem

minimize 5x²
+5y²
−xy −11x+11y +11

a) Find a point satisfying the first-order necessary conditions for a solution.

b) Show that this point is a global minimum. c) What would be the rate of convergence of steepest descent for this problem? d) Starting at x = y = 0, how many steepest descent iterations would it take (at most) to reduce the function value to 10⁻¹¹?