[dplarson]

For numerical optimization, a couple good textbooks are:

- "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

[laichzeit0]

What would you recommend for multi-objective non-convex optimization?

[wenc]

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-...