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

In this paper, we establish the local superlinear convergence property ofsome polynomial-time interior-point methods for an important family of conicoptimization problems. The main structural property used in our analysis is thelogarithmic homogeneity of self-concordant barrier function, which must have{\em negative curvature}. We propose a new path-following predictor-correctorscheme, which work only in the dual space. It is based on an easily computablegradient proximity measure, which ensures an automatic transformation of theglobal linear rate of convergence to the local superlinear one under some mildassumptions. Our step-size procedure for the predictor step is related to themaximum step size maintaining feasibility. As the optimal solution set isapproached, our algorithm automatically tightens the neighborhood of thecentral path proportionally to the current duality gap.

Local Superlinear Convergence of Polynomial-Time Interior-Point Methods for Hyperbolic Cone Optimization Problems