Nonconvex optimization doesn't have the same depth of theoretical underpinnings or canonical body of knowledge as convex optimization so I don't imagine there's a textbook on it that would be authoritative. In the universe of optimization, convex optimization is a special case (linear optimization in turn is a special case of convex); non-convex optimization is everything else!

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-...