Any comprehensive books on global smooth optimization?

Question

Can you share any information about books that review most of the existing numerical methods for global minimization of a multivariable objective function? The objective and constraints are assumed to be smooth, I'm not into integer programming of any type at the moment.

I'm aware of many local optimization methods, such as steepest descent, Newton and quasi-Newton, conjugate gradients, trust-region methods, etc. But currently I would like to learn some practical ones used specifically for global minimization. Equality and inequality constraints are assumed. Most information I find comes in form of narrow-focused academic papers that are disconnected from each other. Thanks!

Answer 1

Try "Metaheuristics". Simulated Annealing, Genetic Algorithm, Tabu search, Ant colony algorithm, swarm intelligence and so on. There will be many books, but I do not know which book is best.

Answer 2

There aren't very many (reasonably-priced) books on the subject in my opinion. A nice survey article is here:

@article{BOUKOUVALA2016701,

title = "Global optimization advances in Mixed-Integer Nonlinear Programming, MINLP, and Constrained Derivative-Free Optimization, CDFO",

journal = "European Journal of Operational Research",

volume = "252",

number = "3",

pages = "701 - 727",

year = "2016",

issn = "0377-2217",

doi = "https://doi.org/10.1016/j.ejor.2015.12.018",

url = "http://www.sciencedirect.com/science/article/pii/S037722171501142X",

author = "Fani Boukouvala and Ruth Misener and Christodoulos A. Floudas",

}

It explains the main modern methods in teh state of the art solvers like BARON, Antigone, and SCIP.

Shamelessly self-promoting, you might also check out Chapter 5 of our Acta Numerica article.

https://www.cambridge.org/core/journals/acta-numerica/article/mixedinteger-nonlinear-optimization/2D0CE8CDA53363A31ADE8689565517BD

Hope this helps!