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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.2010-12-14
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    @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. ( http://mathoverflow.net/questions/49379/finding-3-dimentional-b-spline-controll-points-from-given-array-of-points-from-sp )2010-12-14
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    ...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.2010-12-14

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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://bookstore.siam.org/SE23.

A chapter of Tim Kelley's previous book also talks about implicit filtering and direct search: http://bookstore.siam.org/FR18 (see also http://www.siam.org/books/kelley/fr18).

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://bookstore.siam.org/mp08. 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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    It seems that most of your links to books are broken (or perhaps they are just temporarily not working). If you'd ever like to fix the links I'd be interested in checking out the books.2017-04-14
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    @littleO Done! Thanks for pointing that out!2017-04-17
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    Thanks! Not to bug you, but there are also some broken links here: https://math.stackexchange.com/a/296785/401192017-04-17
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    @littleO and done! Thanks.2017-04-23