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, elliptic control problems with integral constraint on thegradient of the state and box constraints on the control are considered. Theoptimal conditions of the problem are proved. To numerically solve the problem,we use the 'First discretize, then optimize' approach. Specifically, wediscretize both the state and the control by piecewise linear functions. Tosolve the discretized problem efficiently, we first transform it into amulti-block unconstrained convex optimization problem via its dual, then weextend the inexact majorized accelerating block coordinate descent (imABCD)algorithm to solve it. The entire algorithm framework is called finite elementduality-based inexact majorized accelerating block coordinate descent(FE-dABCD) algorithm. Thanks to the inexactness of the FE-dABCD algorithm, eachsubproblems are allowed to be solved inexactly. For the smooth subproblem, weuse the generalized minimal residual (GMRES) method with preconditioner toslove it. For the nonsmooth subproblems, one of them has a closed form solutionthrough introducing appropriate proximal term, another is solved combiningsemi-smooth Newton (SSN) method. Based on these efficient strategies, we provethat our proposed FE-dABCD algorithm enjoys $O(\frac{1}{k^2})$ iterationcomplexity. Some numerical experiments are done and the numerical results showthe efficiency of the FE-dABCD algorithm.

An FE-dABCD algorithm for elliptic optimal control problems with constraints on the gradient of the state and control