Prove mathematically that j has a unique minimum


Problem:

Optimization

Please see the attached file for the fully formatted problems.

Let be defined for as:

1) Evaluate (upside down Delta) Jx.

2) Calculate HessJx .

3) Prove mathematically that J has a unique minimum.

4) a) We are given . Describe the algorithm of the gradiant of optimal step for this function J.

b) Prove mathematically that .

c) Deduce the scalar equation that needs to be solved at each iteration in order to obtain the step.

Attachment:- Equations.rar

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Mathematics: Prove mathematically that j has a unique minimum
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