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 present two globally convergent Levenberg-Marquardt methods for findingzeros of H\"{o}lder metrically subregular mappings that may have non-isolatedzeros. The first method unifies the Levenberg- Marquardt direction and anArmijo-type line search, while the second incorporates this direction with anonmonotone trust-region technique. For both methods, we prove the globalconvergence to a first-order stationary point of the associated merit function.Furthermore, the worst-case global complexity of these methods are provided,indicating that an approximate stationary point can be computed in at most$\mathcal{O}(\varepsilon^{-2})$ function and gradient evaluations, for anaccuracy parameter $\varepsilon>0$. We also study the conditions for theproposed methods to converge to a zero of the associated mappings. Computing amoiety conserved steady state for biochemical reaction networks can be cast asthe problem of finding a zero of a H\"{o}lder metrically subregular mapping. Wereport encouraging numerical results for finding a zero of such mappingsderived from real-world biological data, which supports our theoreticalfoundations.

Finding Zeros of H\"{o}lder Metrically Subregular Mappings via Globally Convergent Levenberg-Marquardt Methods