A variational inequality based stochastic approximation for estimating the flexural rigidity in random fourth-order models

被引：6

作者：

Jadamba, Baasansuren ^{[1
]}

Khan, Akhtar A. ^{[1
]}

Raciti, Fabio ^{[2
]}

Sama, Miguel ^{[3
]}

机构：

[1] Rochester Inst Technol, Sch Math Sci, Rochester, NY 14623 USA

[2] Univ Catania, Dept Math & Comp Sci, Viale A Doria 6, I-95125 Catania, Italy

[3] Univ Nacl Educ Distancia, Dept Matemat Aplicada, Calle Juan del Rosal 12, Madrid 28040, Spain

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2022年 / 111卷

基金：

美国国家科学基金会;

关键词：

Inverse problem; Output least-squares; Energy least-squares; Stochastic approximation; INVERSE PROBLEMS; PDE OPTIMIZATION; RANDOM PARAMETER; COLLOCATION; FRAMEWORK; CONVERGENCE;

D O I：

10.1016/j.cnsns.2022.106406

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper develops a stochastic approximation approach for estimating the flexural rigidity in the framework of variational inequalities. The nonlinear inverse problem is analyzed as a stochastic optimization problem using an energy least-squares formulation. A necessary and sufficient optimality condition for the optimization problem is a stochastic variational inequality solved by a stochastic auxiliary problem principle-based iterative scheme. Exhaustive convergence analysis for the proposed iterative scheme is given under quite general conditions on the random noise. Detailed computational results demonstrate the feasibility and the efficacy of the proposed methodology. (C) 2022 Elsevier B.V. All rights reserved.

引用

页数：11

共 38 条

[1] Mean-Variance Risk-Averse Optimal Control of Systems Governed by PDEs with Random Parameter Fields Using Quadratic Approximations [J].