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

We introduce the GEneralized Newton Inexact Operator Splitting solver(GeNIOS) for large-scale convex optimization. GeNIOS speeds up ADMM byapproximately solving approximate subproblems: it uses a second-orderapproximation to the most challenging ADMM subproblem and solves it inexactlywith a fast randomized solver. Despite these approximations, GeNIOS retains theconvergence rate of classic ADMM and can detect primal and dual infeasibilityfrom the algorithm iterates. At each iteration, the algorithm solves apositive-definite linear system that arises from a second-order approximationof the first subproblem and computes an approximate proximal operator. GeNIOSsolves the linear system using an indirect solver with a randomizedpreconditioner, making it particularly useful for large-scale problems withdense data. Our high-performance open-source implementation in Julia allowsusers to specify convex optimization problems directly (with or without conicreformulation) and allows extensive customization. We illustrate GeNIOS'sperformance on a variety of problem types. Notably, GeNIOS is more than tentimes faster than existing solvers on large-scale, dense problems.

GeNIOS: an (almost) second-order operator-splitting solver for large-scale convex optimization