Nonlocal Continuum Limits of p-Laplacian Problems on Graphs (Elements in Non-local Data Interactions: Foundations and Applications)

El Bouchairi, Imad/ Fadili, Jalal/ Hafiene, Yosra

Cambridge University Press（2023/05発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 124 p.
• 言語 ENG
• 商品コード 9781009327855
• DDC分類 511.5

Full Description

In this Element, the authors consider fully discretized p-Laplacian problems (evolution, boundary value and variational problems) on graphs. The motivation of nonlocal continuum limits comes from the quest of understanding collective dynamics in large ensembles of interacting particles, which is a fundamental problem in nonlinear science, with applications ranging from biology to physics, chemistry and computer science. Using the theory of graphons, the authors give a unified treatment of all the above problems and establish the continuum limit for each of them together with non-asymptotic convergence rates. They also describe an algorithmic framework based proximal splitting to solve these discrete problems on graphs.

Contents

1. Introduction; 2. Mathematical Background; 3. Nonlocal p-Laplacian evolution problem on graphs; 4. Nonlocal p-Laplacian variational problem on graphs; 5. Nonlocal p-Laplacian Dirichlet problem on graphs; 6. Algorithmic framework based on proximal splitting; References.