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I need to understend how black box optimizer work. I need a real life example of how it hlps. So what I need: What was the task, what were parameters, what was the function to minimize and how it all worked toogether. I need deteiled info on this topic, please - wiki does not give lot of help...

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There are so many algorithms that have radically different philosophies... pick one and we'll start there. Otherwise, your question's too broad. –  J. M. Dec 14 '10 at 13:20
    
@J.M. I have such case: 3d points (locations) and weights of the control points (single numbers) of Non-uniform rational B-spline shall be parameters, function to minimize is something like the error volume between the surface created by spline and given array of points. ( mathoverflow.net/questions/49379/… ) –  Kabumbus Dec 14 '10 at 16:00
    
...I was talking about the optimization algorithm. The NURBS is a different matter, and I've seen your question both in here and MO. I would merely say that if your control points are noisy, then NURBS might not be the appropriate approach. –  J. M. Dec 14 '10 at 16:03

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Chapter 10 of Numerical Recipes has a good description of how the golden section search works in 1D, as well as description of multidimensional cases. You could see figure 10.1.1 in the obsolete C version (available free online)

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Your question is quite broad but Tim Kelley's recent book may illuminate you as far as applications are concerned and one type of algorithm (implicit filtering): http://www.ec-securehost.com/SIAM/SE23.html

A chapter of Tim Kelley's previous book also talks about implicit filtering and direct search: http://www.ec-securehost.com/SIAM/FR18.html

A number of algorithms are detailed in the book by Conn, Scheinberg and Vicente, "Introduction to Derivative-Free Optimization" but this book doesn't have many applications: http://www.ec-securehost.com/SIAM/MP08.html From the algorithmic and theoretical point of view, this is a strong book.

This is much more representative of recent research and state of the art than Numerical Recipes.

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