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Because most, if not all, machine learning algorithms can be viewed as minimizing a combination of prediction error penalties and complexity penalties, optimization algorithms are widely needed. Here are some:
* Nelder-Mead
* Gradient descent
* L-BFGS
* Newton's method
If you are interested in learning about optimization, you should read
* Nocedal and Wright
* Boyd and Vanderbergh
Don't bother with other books until you've mastered the material in those two.