Question: (First Order Methods) (a) Define Lipschitz continuity. Explain why this is an important property for a domain to have when first order methods are used.

(First Order Methods)

(a) Define Lipschitz continuity. Explain why this is an important property for a domain to have when first order methods are used. (6 marks)

(b) Given the function f(x) = x3 2x2 + 1 and an x1 of 3 calculate the first three iterations of the Gradient Descent method. You may assume that gamma has a value of 0.001. All calculations must be rounded to four digits of precision

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