On the limited memory BFGS method for large scale optimization
Mathematical Programming: Series A and B
A limited memory algorithm for bound constrained optimization
SIAM Journal on Scientific Computing
Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization
ACM Transactions on Mathematical Software (TOMS)
An analysis of operator splitting techniques in the stiff case
Journal of Computational Physics
Application of higher order derivatives to parameterization
Automatic differentiation of algorithms
The Adjoint Newton Algorithm for Large-Scale Unconstrained Optimization in Meteorology Applications
Computational Optimization and Applications
Enriched Methods for Large-Scale Unconstrained Optimization
Computational Optimization and Applications
Cheap Second Order Directional Derivatives of Stiff ODE Embedded Functionals
SIAM Journal on Scientific Computing
Adjoint sensitivity analysis of regional air quality models
Journal of Computational Physics
A New Conjugate Gradient Method with Guaranteed Descent and an Efficient Line Search
SIAM Journal on Optimization
Predicting air quality: Improvements through advanced methods to integrate models and measurements
Journal of Computational Physics
On the discrete adjoints of adaptive time stepping algorithms
Journal of Computational and Applied Mathematics
SpringSim '10 Proceedings of the 2010 Spring Simulation Multiconference
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Atmospheric chemical transport models (CTMs) are essential tools for the study of air pollution, for environmental policy decisions, for the interpretation of observational data, and for producing air quality forecasts. Many air quality studies require sensitivity analyses, i.e., the computation of derivatives of the model output with respect to model parameters. The derivatives of a cost functional (defined on the model output) with respect to a large number of model parameters can be calculated efficiently through adjoint sensitivity analysis. While the traditional (first order) adjoint models give the gradient of the cost functional with respect to parameters, second order adjoint models give second derivative information in the form of products between the Hessian of the cost functional and a vector (representing a perturbation in sensitivity analysis, a search direction in optimization, an eigenvector, etc.). In this paper we discuss the mathematical foundations of the discrete second order adjoint sensitivity method and present a complete set of computational tools for performing second order sensitivity studies in three-dimensional atmospheric CTMs. The tools include discrete second order adjoints of Runge-Kutta and of Rosenbrock time stepping methods for stiff equations together with efficient implementation strategies. Numerical examples illustrate the use of these computational tools in important applications like sensitivity analysis, optimization, uncertainty quantification and the calculation of directions of maximal error growth in three-dimensional atmospheric CTMs.