Alan L. Yuille, Anand Rangarajan
We introduce the Concave-Convex procedure (CCCP) which con(cid:173) structs discrete time iterative dynamical systems which are guar(cid:173) anteed to monotonically decrease global optimization/energy func(cid:173) tions. It can be applied to (almost) any optimization problem and many existing algorithms can be interpreted in terms of CCCP. In particular, we prove relationships to some applications of Legendre transform techniques. We then illustrate CCCP by applications to Potts models, linear assignment, EM algorithms, and Generalized Iterative Scaling (GIS). CCCP can be used both as a new way to understand existing optimization algorithms and as a procedure for generating new algorithms.