Speaker：Hongpeng Sun, Renmin University of China

Title: Analysis of Fully Preconditioned ADMM with Relaxation in Hilbert Spaces with Applications to Imaging

Abstract: 
Alternating direction method of multipliers (ADMM) is a powerful first order 
methods for various applications in inverse problems and imaging. However, 
there is no clear result on the weak convergence of ADMM in infinite 
dimensional Hilbert spaces and its relaxation studied by Eckstein and 
Bertsakas. In this talk, by employing a kind of partial gap analysis, we prove 
the weak convergence of general preconditioned and relaxed ADMM in 
infinite dimensional Hilbert spaces, with preconditioning for solving all the 
involved implicit equations under mild conditions. We also give the 
corresponding ergodic convergence rates respecting to the partial gap 
function. Numerical tests also show the efficiency of the proposed 
overrelaxation variants of preconditioned ADMM for basic imaging problems.