Question: NLP problem is given as below. Min z(x 1 , x 2 ) = x 1 2 22x 1 + x 2 2 + 4x

NLP problem is given as below.

Min z(x1, x2) = x12 22x1 + x22 + 4x2

Subject to (x1 3)2 (x2 4)2 25

a. Find the set of feasible direction and set of improving direction at point (7,1).

b. According to the solution of a, did point (7,1) meet the necessary conditions to become local min? Why?

c. Find Hessian matrix at point (7,1). What inference is possible based on this Hessian matrix?

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