Reddit mentions of Numerical Recipes in C: The Art of Scientific Computing, Second Edition

If your primary goal for learning C is performance, then I would stop and back up. Matlab is going to be able to do matrix operations faster than your hand written C, because it knows tons of tricks to get performance out of hardware. Scipy as well will give you access to libraries like LAPACK and BLAS that are already highly optimized for those specialized types of computations and run at native speed. And implementing a solver/algorithm in Matlab or Python is going to be much easier and require less programmer time than doing the equivalent in bare C. Turning to C should be a reactive decision ("I have a working model in Matlab but it takes too long to execute") and not pro-active ("I heard C was the fastest, so I'll start there.")

If you really want books on C, then try Numerical Recipes in C: The Art of Scientific Computing. But I must warn you, most of the code in this book and others like it is simply ghastly. It is written by and for scientists, not programmers, with an emphasis on getting things done without regard for "code smell" or modern programming practice. It is the last thing you want to learn C or any other language from.

You can try just googling python for physics pdf files to help get you started. I found these two places which look like a good start. Python is a fairly simple language I would say and most of the research I did with python I learned pretty much on the spot since the application of python to physics is so varied. There are also a lot of really good textbooks out there not just for python, but I feel once you know C or something you can easily figure out python.

Also the bible when it comes to physics computations is this book. It's written in C, I believe there is one for Java, but like I said if you learn C picking up Python should be pretty simple. You might find it online somewhere. I should also add that this is a bible in helping you write pseudo-code algorithms for solving multiple types of mathematical expressions - translating the pseudo-code into actual code is where the learning process coding comes into play.

• graphics gems series
  http://www.amazon.com/gp/aw/d/0122861655
  
  
• numerical recipes in C
  http://www.amazon.com/gp/aw/d/0521431085
  
  
• anything by Jim Blinn

Since you are a practicing engieer with plenty of experience, I will suggest the right way to learn rather than the speed-of-the-internet , show-me-a-web-page way to acquire jargon.

Buy and read textbooks.

Start with Numerical Recipes by Press et al (Link 1). It has a couple of chapters on optimization and some very VERY excellent discussion. It will teach you the way academics formulate these problems, and how they solve them today.

Then read Gill, Murray, and Wright "Practical Optimization" (Link 2).

Next comes Roger Fletcher, "Practical Methods of Optimization". This book has been published two different ways: as a single volume, and also split into two volumes. Since Amazon Used Books sells the two volumes for considerably less money, I recommend that path: (Link 3) and (Link 4) .

After you have read those books, you will be able to appreciate the following paragraph:

I myself have found, in practice, that some of the old 1960's approaches to optimization work DELIGHTFULLY WELL on 2015 real world engineering problems, using 2015 computer power. In fifty years the problems have become 10,000 times more difficult and the computers have become 2^(50/3) times more powerful. The computers are winning the tug of war.

Make an honest try to solve your problem using no-derivative unconstrained optimizers, plus penalty functions or barrier functions for the constraints. I think you will be very pleasantly surprised. If you have honestly done your best and tried your hardest to get this to work, and failed, then your fallback is to implement the full stochastic miasma. Start with the TOMS paper by Corana, Marchesi, Martini, and Ridella. It is the most engineering-results oriented discussion I know of. If you are a masochist, try (just try!) to read the various publications and white papers by Lester Ingber. You will regret it.