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    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.

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    Let be defined for X=(x,y) as

    1) Evaluate ;

    2) Calculate Hessian HessJ(X);
    3) Prove mathematically J has a unique minimum;
    Proof. Since HessJ(X)= , we know that
    and . So HessJ(X) is a definite matrix . So, J has a unique minimum.
    4) a)We are given a . Describe the algorithm of ...

    Solution Summary

    Optimization questions are answered. The expert proves mathematical that a function has a unique minimum. The solution is detailed and well presented.