# Optimization

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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.

https://brainmass.com/math/optimization/optimization-evaluated-calculated-11029

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

1) Evaluate ;

2) Calculate Hessian HessJ(X);

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.