J Glob Optim DOI 10.1007/s10898-008-9343-5 Improving the efficiency of DC global optimization methods by improving the DC representation of the objective function Albert Ferrer · Juan Enrique Martínez-Legaz Received: 19 June 2008 / Accepted: 12 August 2008 © Springer Science+Business Media, LLC. 2008 Abstract There are infinitely many ways of representing a d.c. function as a difference of convex functions. In this paper we analyze how the computational efficiency of a d.c.optimi- zation algorithm depends on the representation we choose for the objective function, and we address the problem of characterizing and obtaining a computationally optimal representa- tion. We introduce some theoretical concepts which are necessary for this analysis and report some numerical experiments. Keywords Dc representation · Dc program · Outer approximation · Branch and bound · Semi-infinite program Mathematics Subject Classification (2000) 90C26 · 90C30 1 Introduction Consider a programming problem with d.c. objective function and linear and convex con- straints: minimize f(x) - h(x) subject to Ax ≤ b, ϕ(x) ≤ 0, (1) where A is a real m × n matrix, b ∈ IR m and f , h and ϕ are proper convex functions on IR n . By introducing an additional variable t the program (1) can be transformed into the equivalent convex minimization problem subject to an additional reverse convex constraint A. Ferrer Departament de Matemàtica Aplicada I, Universitat Politècnica de Catalunya, Barcelona, Spain e-mail: alberto.ferrer@upc.edu J. E. Martínez-Legaz (B ) Departament d’Economia i d’Història Econòmica, Universitat Autonoma de Barcelona, Barcelona, Spain e-mail: juanenrique.martinez@uab.es 123