Bregman Three-Operator Splitting Methods

Abstract

The paper presents primal–dual proximal splitting methods for convex optimization, in which generalized Bregman distances are used to define the primal and dual proximal update steps. The methods extend the primal and dual Condat–Vũ algorithms and the primal–dual three-operator (PD3O) algorithm. The Bregman extensions of the Condat–Vũ algorithms are derived from the Bregman proximal point method applied to a monotone inclusion problem. Based on this interpretation, a unified framework for the convergence analysis of the two methods is presented. We also introduce a line search procedure for stepsize selection in the Bregman dual Condat–Vũ algorithm applied to equality-constrained problems. Finally, we propose a Bregman extension of PD3O and analyze its convergence.

Pathways to Ensuring Food Security in the Context of the Chinese Bioeconomy Landscape

“…As for 2020, the output value of sectors such as biopharmaceuticals, biomanufacturing, biobreeding, bioenergy, and bioenvironmental protection in China has approached nearly 5 trillion RMB. The main business revenue of the bio and health industry exceeded 10 trillion RMB . However, the policy framework for China’s bioeconomy is still in its nascent stage, and there is an urgent need to draw up the experience of other countries with mature developments in the field of bioeconomy.…”