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/

Global: Zendy Plus annual

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

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The augmented Lagrangian method (ALM) is a classical optimization tool thatsolves a given "difficult" (constrained) problem via finding solutions of asequence of "easier"(often unconstrained) sub-problems with respect to theoriginal (primal) variable, wherein constraints satisfaction is controlled viathe so-called dual variables. ALM is highly flexible with respect to how primalsub-problems can be solved, giving rise to a plethora of different primal-dualmethods. The powerful ALM mechanism has recently proved to be very successfulin various large scale and distributed applications. In addition, severalsignificant advances have appeared, primarily on precise complexity resultswith respect to computational and communication costs in the presence ofinexact updates and design and analysis of novel optimal methods fordistributed consensus optimization. We provide a tutorial-style introduction toALM and its variants for solving convex optimization problems in large scaleand distributed settings. We describe control-theoretic tools for thealgorithms' analysis and design, survey recent results, and provide novelinsights in the context of two emerging applications: federated learning anddistributed energy trading.

Primal-dual methods for large-scale and distributed convex optimization and data analytics