2005/12/01 by Luc Pronzato, Henry P. Wynn, Anatoly Zhigljavsky +1 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Optimization Algorithms Research #Optimization and Variational Analysis #Topology Optimization in Engineering #math.OC #msc:68Q25 #msc:90C25
paper · pdf · doi:10.1007/s10107-005-0602-7
published as Mathematical Programming, Series A 107 (2006) 409-438 · The original publication is available at http://www.springerlink.com
openalex publication_date 2005/12/01 · arxiv created 2008/02/29 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/02
The asymptotic behaviour of a family of gradient algorithms (including the methods of steepest descent and minimum residues) for the optimisation of bounded quadratic operators in Rd and Hilbert spaces is analyzed. The results obtained generalize those of Akaike (1959) in several directions. First, all algorithms in the family are shown to have the same asymptotic behaviour (convergence to a two-point attractor), which implies in particular that they have similar asymptotic convergence rates. Second, the analysis also covers the Hilbert space case. A detailed analysis of the stability property of the attractor is provided.