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

We study a class of monotone inclusions called "self-concordant inclusion"which covers three fundamental convex optimization formulations as specialcases. We develop a new generalized Newton-type framework to solve thisinclusion. Our framework subsumes three schemes: full-step, damped-step andpath-following methods as specific instances, while allows one to use inexactcomputation to form generalized Newton directions. We prove a local quadraticconvergence of both the full-step and damped-step algorithms. Then, we proposea new two-phase inexact path-following scheme for solving this monotoneinclusion which possesses an$\mathcal{O}\left(\sqrt{\nu}\log(1/\varepsilon)\right)$-worst-caseiteration-complexity to achieve an $\varepsilon$-solution, where $\nu$ is thebarrier parameter and $\varepsilon$ is a desired accuracy. As byproducts, wecustomize our scheme to solve three convex problems: convex-concavesaddle-point, nonsmooth constrained convex program, and nonsmooth convexprogram with linear constraints. We also provide three numerical examples toillustrate our theory and compare with existing methods.

Self-concordant inclusions: A unified framework for path-following generalized Newton-type algorithms