# Solving Composite Monotone Inclusions in Reflexive Banach Spaces by Constructing Best Bregman Approximations from Their Kuhn-Tucker Set

arXiv: https://arxiv.org/abs/1505.00362 · HTML: https://mlsanity.com/paper/1505.00362/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 May 2015.

## Built on by (most cited first, 1 of 1)

- [A Stochastic Bregman Primal-Dual Splitting Algorithm for Composite Optimization](https://mlsanity.com/paper/2112.11928/) (2021)

## Abstract (arXiv)

We introduce the first operator splitting method for composite monotone inclusions outside of Hilbert spaces. The proposed primal-dual method constructs iteratively the best Bregman approximation to an arbitrary point from the Kuhn-Tucker set of a composite monotone inclusion. Strong convergence is established in reflexive Banach spaces without requiring additional restrictions on the monotone operators or knowledge of the norms of the linear operators involved in the model. The monotone operators are activated via Bregman distance-based resolvent operators. The method is novel even in Euclidean spaces, where it provides an alternative to the usual proximal methods based on the standard distance.