Prove that VV () = 0 is a necessary condition for optimality in an unconstrained problem min {V(r) subject to rR"), V: R" R, CR" Why is this condition not sufficient ? Question 7. (3) Provide a pseudo -code (schematic diagram) for a conjugate gradient algorithm Explain each step of the algorithm Does the conjugate gradient algorithm apply to the same class of problems as the steepest descent ? Why is it better that the steepest descent ? Question 8. Provide a rationale for the Newton search direction algorithm by discussing the derivation of the New- ton search direction Comment on the class of problems to which it applies. Describe in detail the modifications of the Newton algorithm, specifically the Pseudo -Newton (or P-algorithm) and the Secant algorithm Question 9. Write a pseudo-code for some version of the Secant algorithm Question 10. Describe in detail the Armijo step size rule and write a pseudo-code for it.