This paper is a summary of the author's Ph.D. thesis in Mathematics supervised by Giancarlo Bigi and Antonio Frangioni, and defended on 23 June 2008 at the Università di Pisa. The thesis is written in English and available from http://www.di.unipi.it/di/groups/optimize. The work deals with outer approximation algorithms for solving an alternative equivalent formulation and a novel generalization of canonical DC (difference of convex) programs. The thesis develops an in-depth investigation of structural properties of both problems, and of the impact of approximations onto the quality of approximate optimal solutions. It also propose hierarchies of conditions guaranteeing convergence and develops several different implementable algorithms for canonical DC programs and its novel generalization, respectively.
