Optimal Control of Stochastic Variational Inequalities

被引：0

作者：

Grecksch, Wilfried ^{[1
]}

Khan, Akhtar A. ^{[2
]}

Sama, Miguel ^{[3
]}

Tammer, Christiane ^{[1
]}

机构：

[1] Martin Luther Univ Halle Wittenberg, Inst Math, Halle, Germany

[2] Rochester Inst Technol, Sch Math Sci, Rochester, NY USA

[3] Univ Nacl Educ Distancia, Dept Matemat Aplicada, Madrid, Spain

来源：

MINIMAX THEORY AND ITS APPLICATIONS | 2024年 / 9卷 / 01期

关键词：

Stochastic optimal control; partial differential equations with random data; stochastic approximation; regularization; penalization; BOUNDARY-VALUE-PROBLEMS; INVERSE PROBLEMS; COLLOCATION; CONSTRAINTS;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This work focuses on the optimal control problem for elliptic stochastic variational inequalities where the diffusivity coefficient and the source term are random fields. Besides recalling the existence theorem for the stochastic elliptic variational inequalities, we also give an existence result for the optimal control problem, which is posed as a stochastic optimization problem. We conduct two preliminary computational experiments by coupling the penalty method with the stochastic approximation approach.

引用

页码：117 / 128

页数：12

共 30 条

[1] A variational-inequality approach to stochastic boundary value problems with inequality constraints and its application to contact and elastoplasticity [J].

Arnst, M. ;

Ghanem, R. .

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2012, 89 (13) :1665-1690

[2] Use of augmented Lagrangian methods for the optimal control of obstacle problems [J].

Bergounioux, M .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1997, 95 (01) :101-126

[3] Gradient-based estimation of uncertain parameters for elliptic partial differential equations [J].

Borggaard, Jeff ;

van Wyk, Hans-Werner .

INVERSE PROBLEMS, 2015, 31 (06)

[4] Multilevel and weighted reduced basis method for stochastic optimal control problems constrained by Stokes equations [J].

Chen, Peng ;

Quarteroni, Alfio ;

Rozza, Gianluigi .

NUMERISCHE MATHEMATIK, 2016, 133 (01) :67-102

[5]

De los Reyes J.C., 2015, Numerical PDE-Constrained Optimization

[6] A polynomial chaos approach to stochastic variational inequalities [J].

Forster, R. ;

Kornhuber, R. .

JOURNAL OF NUMERICAL MATHEMATICS, 2010, 18 (04) :235-255

[7] PROJECTED STOCHASTIC GRADIENTS FOR CONVEX CONSTRAINED PROBLEMS IN HILBERT SPACES [J].

Geiersbach, Caroline ;

Pflug, Georg Ch .

SIAM JOURNAL ON OPTIMIZATION, 2019, 29 (03) :2079-2099

[8] A class of random variational inequalities and simple random unilateral boundary value problems - Existence, discretization, finite element approximation [J].

Gwinner, J .

STOCHASTIC ANALYSIS AND APPLICATIONS, 2000, 18 (06) :967-993

[9]

Gwinner J., 2021, Uncertainty Quantification in Variational Inequalities: Theory, Numerics, and Applications

[10]

Gwinner J, 2018, J CONVEX ANAL, V25, P545

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