Q1: Consider the function f: R2 → R given by f(x1, x₂) (a) Find all stationary points of f. mum/maximum or a saddle point. x²₁x₁x₂ + x² + x₁-x2. Classify each point, i.e., determine if it is a local mini- (b) Starting at x = (0,0), find the local minimum of f using Newton's method (algorithm below). Stop when ||Vf(x, ak)|| <0.01. For the optimal step size use Matlab or similar to find the minimum of g(a) = f(x*+adk). You may also use Matlab or similar to work with the gradient and Hessian of f. [15 marks] Newton's Method 1: Start from an initial point º, set k=0. 2: If (Vf(x) < ) then exit. If V2f(a) is positive definite then dk-[V2 f(x)]-¹Vf(x) else dk = -f(x). 3: Calculate ak = minazo f(x + adk). 4: Set æk+1=k+ad and k=k+1 then return to step 2.

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q1 consider the function f r2 r given by f x1 x a find all stationary

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Q1: Consider the function f: R2 → R given by f(x1, x₂) (a) Find all stationary points of f. mum/maximum or a saddle point. x²₁x₁x₂ + x² + x₁-x2. Classify each point, i.e., determine if it is a local mini- (b) Starting at x = (0,0), find the local minimum of f using Newton's method (algorithm below). Stop when ||Vf(x, a