The degenerate variable metric proximal point algorithm and adaptive stepsizes for primal-dual Douglas-Rachford

• Published in: Optimization Vol. 74; no. 6; pp. 1355 - 1381
• Main Authors: Lorenz, Dirk A., Marquardt, Jannis, Naldi, Emanuele
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 26.04.2025; Taylor & Francis LLC
• Subjects: Adaptive algorithms; adaptive stepsizes; Algorithms; Convergence; Douglas-Rachford method; non-stationary primal-dual method; Preconditioned proximal point algorithm; varying preconditioners

In this paper, the degenerate preconditioned proximal point algorithm will be combined with the idea of varying preconditioners leading to the degenerate variable metric proximal point algorithm. The weak convergence of the resulting iteration will be proven. From the perspective of the degenerate v...