It's kind of like convex optimization is English, and nonconvex optimization is non-English. I'm not sure it's possible to write a text on non-English.
That doesn't non-convex optimization problems are unsolvable, merely that there are many different attacks that aren't necessarily coherently linked. A few common ones include:
a) convex reformulation, where possible.
b) partitioning into convex regions (used in global optimization)
c) heuristic/evolutionary approaches
d) specialized approaches for particular problem structures like integer programs, complementarity problems etc. (there are good textbooks for these)
There are a few good surveys of the landscape however. Most are journal pubs. This text [1] seems to be a good one.
[1] https://www.amazon.com/Nonlinear-Mixed-Integer-Optimization-...
- "Practical Optimization" by P. E. Gill, W. Murray and M. H. Wright: a little old (1982), but provides a solid foundation
- "Convex Optimization" by S. Boyd and L. Vandenberghe: the standard for learning convex optimization (also available as a free PDF from the author's website)
- "Convex Analysis and Monotone Operator Theory in Hilbert Spaces" by H. H. Bauschke and P. L. Combettes: covers a more specialized area of numerical optimization, but the notation is beautiful (IMO) and it acts as a useful reference for recent research on, e.g., operator splitting methods