English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

The Douglas-Rachford algorithm (DRA) is a powerful optimization method forminimizing the sum of two convex (not necessarily smooth) functions. The vastmajority of previous research dealt with the case when the sum has at least oneminimizer. In the absence of minimizers, it was recently shown that for thecase of two indicator functions, the DRA converges to a best approximationsolution. In this paper, we present a new convergence result on the the DRAapplied to the problem of minimizing a convex function subject to a linearconstraint. Indeed, a normal solution may be found even when the domain of theobjective function and the linear subspace constraint have no point in common.As an important application, a new parallel splitting result is provided. Wealso illustrate our results through various examples.

On the behaviour of the Douglas-Rachford algorithm for minimizing a convex function subject to a linear constraint