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 problem of finding roots or solutions of a nonlinear partial differentialequation may be formulated as the problem of minimizing a sum of squaredresiduals. One then defines an evolution equation so that in the asymptoticlimit a minimizer, and often a solution of the PDE, is obtained. Thecorresponding discretized nonlinear least squares problem is an often metproblem in the field of numerical optimization, and thus there exist a widevariety of methods for solving such problems. We review here Newton's methodfrom nonlinear optimization both in a discrete and continuous setting andpresent results of a similar nature for the Levernberg-Marquardt method. Weapply these results to the Ginzburg-Landau model of superconductivity.

Nonlinear optimization in Hilbert space using Sobolev gradients with applications