Global optimization. Theory, algorithms, and applications (Q2864120)

This monograph give a comprehensive overview over recent developments in global optimization. It starts with results about complexity, verifying the difficulties of computing a global optimum on a computer. Nicely, a global optimum can (sometimes) be approximated using (fully) polynomial time approximation schemes. The next topic are procedures for computing upper bounds for the global optimal value. Here, deterministic methods as descent or local search algorithms, random search, (meta)heuristics as particle swarm algorithm or simulated annealing and others, are shortly considered. Investigated are also smoothing methods. A larger subsection is devoted to problems where it is comprehensive to calculate function values. The next question is the calculation of lower bounds for the global optimum. Here, the \(\alpha\)-BB method, Lipschitz optimization, interval arithmetic and many, many other methods can be found. Combining methods for computing upper bounds with approaches to compute lower bounds, branch-and-bound algorithms are then developed. Of special interest can some finiteness results be. Over 30 pages with references conclude the monograph. Summing up, this is a very helpful monograph for all who are interested in global optimization or need to find a global optimum in some application but also for beginners in the field of global optimization.