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Powells Search Method Example

The attached file has some slides provided by my professor on the univariate method and powell's method. I am having trouble understanding, so I tried to work an example, but I am not getting very far.

As you work the example, could you explain each step as you go. My professor tried but he and I both ended up frustrated, and I ended up more confused.

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Thanks so much for your interest. Please read my explanations carefully and do not hesitate to tocontact me if there is any vagueness. Good Luck.

Well, let's consider the function:

We want to maximize this function using Powell's search method. I am going to explain the method for you through this example and I will not necessarily be loyal to the notation used by your instructor. If you learn the algorithm, then you can solve any given problem. Please let me know if there is any vagueness.

Ok, so we have:

Then we choose two linearly independent vectors. The most natural and probably best choices are the standard vectors.
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Solution Summary

The expert examines Powell's search method examples. Univariate methods are analyzed.

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