What are good books/articles you would recommend on/for the topic?
I am supposed to write a seminar paper about the topic, and I would appreciate any books or articles that would introduce me to the topic, from where I could continue writing on my own. So far, I've only found two papers and one of which is computer-science-oriented, and other is from Stanford and only discusses the topic. I appreciate any help.
P.S. the seminar paper should contain from fifteen up to twenty pages, or even more.
P.P.S. it seams as I should start learning Russian, for only Russians delve into these areas.
You could start here. The site helps you choose an optimization algorithm according to problem type. One of the problem types listed is "derivative free" optimization. There are many references.
Also, bear in mind that some optimization packages that require derivatives also include utilities for estimating these. The donlp2 package does this, for example.
For theoretical aspects, you could start with this book.