title: On global and local convergence of half-quadratic algorithms.
abstract: This paper provides original results on the global and local convergence properties of half-quadratic (HQ) algorithms resulting from the Geman and Yang (GY) and Geman and Reynolds (GR) primal-dual constructions. First, we show that the convergence domain of the GY algorithm can be extended with the benefit of an improved convergence rate. Second, we provide a precise comparison of the convergence rates for both algorithms. This analysis shows that the GR form does not benefit from a better convergence rate in general. Moreover, the GY iterates often take advantage of a low cost implementation. In this case, the GY form is usually faster than the GR form from the CPU time viewpoint.
authors: Institut de Recherche en Communications et en Cybernétique de Nantes (IRCCyN), BP 92 101-44321 Nantes Cedex 03, France. marc.allain@irccyn.ec-nantes.fr
authors: Marc
authors: M
authors: Allain
authors: Jerôme
authors: J
authors: Idier
authors: Yves
authors: Y
authors: Goussard