This is a summary of the author's PhD thesis supervised by Andrea Lodi and defended on 16 April 2009 at the University of Bologna. The thesis is written in English and available for download at http://www.or.deis.unibo.it/staff_pages/dambrosio/Phd_Th_DAmbrosio.tar.gz. The main topic of the thesis is Mixed Integer Non-Linear Programming, with focus on non-convex problems (i.e., problems for which the feasible region of the continuous relaxation is a non-convex set) and real-world applications. Different kinds of algorithms are presented: linearization methods, heuristic and global optimization algorithms. Also, different kinds of real-world applications are solved, arising, for example, from Hydraulic and Electrical Engineering problems. The last part of the thesis is devoted to software and tools for mixed integer non-linear programming problems.
