Relaxed proximal point algorithm for monotone inclusion problem beyond monotonicity
Journal of Decision Making and Healthcare, Volume 2, Issue 2, August 2025, Pages: 105–113
GRACE NNENNAYA OGWO
School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, People’s Republic of China
YEKINI SHEHU
School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, People’s Republic of China
Abstract
In this paper, we introduce a relaxed proximal point algorithm for solving the generalized inclusion problem involving a maximally comonotone operator in the framework of real Hilbert spaces. While the classical theory for the proximal point algorithm relies heavily on monotonicity assumptions, we demonstrate how comonotonicity (a weaker yet structurally rich property) provides sufficient conditions for convergence. By exploiting the fundamental connection between comonotonicity and averaged resolvents, we establish weak convergence of our proposed method under standard assumptions.
Cite this Article as
Grace Nnennaya Ogwo and Yekini Shehu, Relaxed proximal point algorithm for monotone inclusion problem beyond monotonicity, Journal of Decision Making and Healthcare, 2(2), 105–113, 2025