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 present a new steepest-descent type algorithm for convexoptimization problems. Our algorithm pieces the unknown into sub-blocs ofunknowns and considers a partial optimization over each sub-bloc. In quadraticoptimization, our method involves Newton technique to compute the step-lengthsfor the sub-blocs resulting descent directions. Our optimization method isfully parallel and easily implementable, we first presents it in a generallinear algebra setting, then we highlight its applicability to a parabolicoptimal control problem, where we consider the blocs of unknowns with respectto the time dependency of the control variable. The parallel tasks, in the lastproblem, turn "on" the control during a specific time-window and turn it "off"elsewhere. We show that our algorithm significantly improves the computationaltime compared with recognized methods. Convergence analysis of the new optimalcontrol algorithm is provided for an arbitrary choice of partition. Numericalexperiments are presented to illustrate the efficiency and the rapidconvergence of the method.

A new approach to improve ill-conditioned parabolic optimal control problem via time domain decomposition