Paper Info
Title
Second-order adjoints for solving PDE-constrained optimization problems
Abstract
In this paper, we discuss the mathematical foundations of SOA sensitivity analysis and show that it provides an efficient approach to obtain Hessian-vector products. We study the benefits of using second-order information in the numerical optimization process for data assimilation applications. The numerical studies are performed in a twin experiment setting with a two-dimensional shallow water model. Different scenarios are considered with different discretization approaches, observation sets, and noise levels. Optimization algorithms that employ second-order derivatives are tested against widely used methods that require only first-order derivatives. Conclusions are drawn regarding the potential benefits and the limitations of using high-order information in large-scale data assimilation problems.
Year
DOI
Venue
2012
10.1080/10556788.2011.610455
Optimization Methods and Software
Keywords
Field
DocType
numerical study,data assimilation application,optimization algorithm,numerical optimization process,second-order derivative,different discretization approach,pde-constrained optimization problem,high-order information,assimilation problem,different scenario,large-scale data,second-order adjoints,inverse problems,first order,shallow water equation,quasi newton method,shallow water,conjugate gradient,data assimilation,inverse problem,shallow water equations,second order,cost function,optimization problem,optimal estimation,constrained optimization,numerical analysis,partial differential equation,sensitivity analysis
Discretization,Mathematical optimization,Mathematical software,Optimization algorithm,Inverse problem,Data assimilation,Constrained optimization problem,Numerical analysis,Shallow water equations,Mathematics
Journal
Volume
Issue
ISSN
27
4-5
1055-6788
Citations 
PageRank 
References 
7
0.73
19
Authors
3
Name
Order
Citations
PageRank
Alexandru Cioaca1163.39
Mihai Alexe2293.48
Adrian Sandu332558.93