caa a22 4500 475769600 CHVBK 20180406123616.0 cr unu---uuuuu 170329e20000601xx s 000 0 eng 10.1007/PL00011373 doi (NATIONALLICENCE)springer-10.1007/PL00011373 On the superlinear convergence of the variable metric proximal point algorithm using Broyden and BFGS matrix secant updating [Elektronische Daten] [J.V. Burke, Maijian Qian] Abstract. : In previous work, the authors provided a foundation for the theory of variable metric proximal point algorithms in Hilbert space. In that work conditions are developed for global, linear, and super-linear convergence. This paper focuses attention on two matrix secant updating strategies for the finite dimensional case. These are the Broyden and BFGS updates. The BFGS update is considered for application in the symmetric case, e.g., convex programming applications, while the Broyden update can be applied to general monotone operators. Subject to the linear convergence of the iterates and a quadratic growth condition on the inverse of the operator at the solution, super-linear convergence of the iterates is established for both updates. These results are applied to show that the Chen-Fukushima variable metric proximal point algorithm is super-linearly convergent when implemented with the BFGS update. Springer-Verlag Berlin Heidelberg, 2000 Key words: maximal monotone operator - proximal point methods - variable metric - global convergence - super-linear convergence nationallicence Burke J.V. Department of Mathematics, Box # 354350, University of Washington, Seattle, Washington 98195-4350, US aut Qian Maijian Department of Mathematics, California State University, Fullerton, CA 92834, US aut https://doi.org/10.1007/PL00011373 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/PL00011373 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Burke J.V. Department of Mathematics, Box # 354350, University of Washington, Seattle, Washington 98195-4350, US aut NATIONALLICENCE 700 1- Qian Maijian Department of Mathematics, California State University, Fullerton, CA 92834, US aut Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer