Results for “Iterative methods” — Page 53

DOE OSTI2016

SU-F-I-36: In-Utero Dose Measurements Within Postmortem Subjects for Estimating Fetal Doses in Pregnant Patients Examined with Pulmonary Embolism, Trauma, and Appendicitis CT

Purpose: The imaging of pregnant patients is medically necessary in certain clinical situations. The purpose of this work was to directly measure uterine doses in a cadaver scanned with CT protocols commonly performed on pregnant patients in order to estimate fetal dose and assess potential risk. Method: One postmortem subject was scanned on a 320-slice CT scanner with standard pulmonary embolism, trauma, and appendicitis protocols. All protocols were performed with the scan parameters and ranges currently used in clinical practice. Exams were performed both with and without iterative reconstruction to highlight the dose savings potential. Optically stimulated luminescent dosimeters (OSLDs) were inserted into the uterus in order to approximate fetal doses. Results: In the pulmonary embolism CT protocol, the uterus is outside of the primary beam, and the dose to the uterus was under 1 mGy. In the trauma and appendicitis protocols, the uterus is in the primary beam, the fetal dose estimates were 30.5 mGy for the trauma protocol, and 20.6 mGy for the appendicitis protocol. Iterative reconstruction reduced fetal doses by 30%, with uterine doses at 21.3 for the trauma and 14.3 mGy for the appendicitis protocol. Conclusion: Fetal doses were under 1 mGy when exposed to scatter radiation, and under 50 mGy when exposed to primary radiation with the trauma and appendicitis protocols. Consistent with the National Council on Radiation Protection & Measurements (NCRP) and the International Commission on Radiological Protection (ICRP), these doses exhibit a negligible risk to the fetus, with only a small increased risk of cancer. Still, CT scans are not recommended during pregnancy unless the benefits of the exam clearly outweigh the potential risk. Furthermore, when possible, pregnant patients should be examined on CT scanners equipped with iterative reconstruction in order to keep patient doses as low as reasonable achievable.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2019

Impact of non-specific normal databases on perfusion quantification of low-dose myocardial SPECT studies

Aim: To evaluate the impact of non-specific normal databases on the percent summed rest score (SR%) and stress score (SS%) from simulated low-dose SPECT studies by shortening the acquisition time/projection. Methods: Forty normal-weight and 40 overweight/obese patients underwent myocardial studies with a conventional gamma-camera (BrightView, Philips) using three different acquisition times/projection: 30, 15, and 8 s (100%-counts, 50%-counts, and 25%-counts scan, respectively) and reconstructed using the iterative algorithm with resolution recovery (IRR) Astonish{sup TM} (Philips). Three sets of normal databases were used: (1) full-counts IRR; (2) half-counts IRR; and (3) full-counts traditional reconstruction algorithm database (TRAD). The impact of these databases and the acquired count statistics on the SR% and SS% was assessed by ANOVA analysis and Tukey test (P < 0.05). Results: Significantly higher SR% and SS% values (> 40%) were found for the full-counts TRAD databases respect to the IRR databases. For overweight/obese patients, significantly higher SS% values for 25%-counts scans (+19%) are confirmed compared to those of 50%-counts scan, independently of using the half-counts or the full-counts IRR databases. Conclusions: Astonish{sup TM} requires the adoption of the own specific normal databases in order to prevent very high overestimation of both stress and rest perfusion scores. Conversely, the count statistics of the normal databases seems not to influence the quantification scores.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2015

Measurement of absolute myocardial blood flow in humans using dynamic cardiac SPECT and 99m Tc-tetrofosmin: Method and validation

The objective of this study was to measure myocardial blood flow (MBF) in humans using 99m Tc-tetrofosmin and dynamic single-photon emission computed tomography (SPECT). Dynamic SPECT using 99m Tc-tetrofosmin and dynamic positron emission tomography (PET) was performed on a group of 16 patients. The SPECT data were reconstructed using a 4D-spatiotemporal iterative reconstruction method. The data corresponding to 9 patients were used to determine the flow-extraction curve for 99m Tc-tefrofosmin while data from the remaining 7 patients were used for method validation. The nonlinear tracer correction parameters A and B for 99m Tc-tefrofosmin were estimated for the 9 patients by fitting the flow-extraction curve K 1 = F(1–Aexp(–B/F)) for K 1 values estimated with 99m Tc-tefrofosmin using SPECT and MBF values estimated with 13 N-NH 3 using PET. These parameters were then used to calculate MBF and coronary flow reserve (CFR) in three coronary territories (LAD, RCA, and LCX) using SPECT for an independent cohort of 7 patients. The results were then compared with that estimated with 13 N-NH 3 PET. The flow-dependent permeability surface-area product (PS) for 99m Tc-tefrofosmin was also estimated. The estimated flow-extraction parameters for 99m Tc-tefrofosmin were found to be A = 0.91 ± 0.11, B = 0.34 ± 0.20 (R 2 = 0.49). The range of MBF in LAD, RCA, and LCX was 0.44-3.81 mL/min/g. The MBF between PET and SPECT in the group of independent cohort of 7 patients showed statistically significant correlation, r = 0.71 (P < .001). However, the corresponding CFR correlation was moderate r = 0.39 yet statistically significant (P = .037). The PS for 99m Tc-tefrofosmin was (0.019 ± 0.10)*MBF + (0.32 ± 0.16). Dynamic cardiac SPECT using 99m Tc-tetrofosmin and a clinical two-headed SPECT/CT scanner can be a useful tool for estimation of MBF.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2015

A dual-view digital tomosynthesis imaging technique for improved chest imaging

Purpose: Digital tomosynthesis (DTS) has been shown to be useful for reducing the overlapping of abnormalities with anatomical structures at various depth levels along the posterior–anterior (PA) direction in chest radiography. However, DTS provides crude three-dimensional (3D) images that have poor resolution in the lateral view and can only be displayed with reasonable quality in the PA view. Furthermore, the spillover of high-contrast objects from off-fulcrum planes generates artifacts that may impede the diagnostic use of the DTS images. In this paper, the authors describe and demonstrate the use of a dual-view DTS technique to improve the accuracy of the reconstructed volume image data for more accurate rendition of the anatomy and slice images with improved resolution and reduced artifacts, thus allowing the 3D image data to be viewed in views other than the PA view. Methods: With the dual-view DTS technique, limited angle scans are performed and projection images are acquired in two orthogonal views: PA and lateral. The dual-view projection data are used together to reconstruct 3D images using the maximum likelihood expectation maximization iterative algorithm. In this study, projection images were simulated or experimentally acquired over 360° using the scanning geometry for cone beam computed tomography (CBCT). While all projections were used to reconstruct CBCT images, selected projections were extracted and used to reconstruct single- and dual-view DTS images for comparison with the CBCT images. For realistic demonstration and comparison, a digital chest phantom derived from clinical CT images was used for the simulation study. An anthropomorphic chest phantom was imaged for the experimental study. The resultant dual-view DTS images were visually compared with the single-view DTS images and CBCT images for the presence of image artifacts and accuracy of CT numbers and anatomy and quantitatively compared with root-mean-square-deviation (RMSD) values computed using the digital chest phantom or the CBCT images as the reference in the simulation and experimental study, respectively. High-contrast wires with vertical, oblique, and horizontal orientations in a PA view plane were also imaged to investigate the spatial resolutions and how the wire signals spread in the PA view and lateral view slice images. Results: Both the digital phantom images (simulated) and the anthropomorphic phantom images (experimentally generated) demonstrated that the dual-view DTS technique resulted in improved spatial resolution in the depth (PA) direction, more accurate representation of the anatomy, and significantly reduced artifacts. The RMSD values corroborate well with visual observations with substantially lower RMSD values measured for the dual-view DTS images as compared to those measured for the single-view DTS images. The imaging experiment with the high-contrast wires shows that while the vertical and oblique wires could be resolved in the lateral view in both single- and dual-view DTS images, the horizontal wire could only be resolved in the dual-view DTS images. This indicates that with single-view DTS, the wire signals spread liberally to off-fulcrum planes and generated wire shadow there. Conclusions: The authors have demonstrated both visually and quantitatively that the dual-view DTS technique can be used to achieve more accurate rendition of the anatomy and to obtain slice images with improved resolution and reduced artifacts as compared to the single-view DTS technique, thus allowing the 3D image data to be viewed in views other than the PA view. These advantages could make the dual-view DTS technique useful in situations where better separation of the objects-of-interest from the off-fulcrum structures or more accurate 3D rendition of the anatomy are required while a regular CT examination is undesirable due to radiation dose considerations.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2016

SU-F-T-463: Light-Field Based Dynalog Verification

Purpose: To independently verify leaf positions in so-called dynalog files for a Varian iX linac with a Millennium 120 MLC. This verification provides a measure of confidence that the files can be used directly as part of a more extensive intensity modulated radiation therapy / volumetric modulated arc therapy QA program. Methods: Initial testing used white paper placed at the collimator plane and a standard hand-held digital camera to image the light and shadow of a static MLC field through the paper. Known markings on the paper allow for image calibration. Noise reduction was attempted with removal of ‘inherent noise’ from an open-field light image through the paper, but the method was found to be inconsequential. This is likely because the environment could not be controlled to the precision required for the sort of reproducible characterization of the quantum noise needed in order to meaningfully characterize and account for it. A multi-scale iterative edge detection algorithm was used for localizing the leaf ends. These were compared with the planned locations from the treatment console. Results: With a very basic setup, the image of the central bank A leaves 15–45, which are arguably the most important for beam modulation, differed from the planned location by [0.38±0.28] mm. Similarly, for bank B leaves 15–45 had a difference of [0.42±0.28] mm Conclusion: It should be possible to determine leaf position accurately with not much more than a modern hand-held camera and some software. This means we can have a periodic and independent verification of the dynalog file information. This is indicated by the precision already achieved using a basic setup and analysis methodology. Currently, work is being done to reduce imaging and setup errors, which will bring the leaf position error down further, and allow meaningful analysis over the full range of leaves.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2011

DAKOTA : a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis.

The DAKOTA (Design Analysis Kit for Optimization and Terascale Applications) toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. DAKOTA contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the DAKOTA toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a theoretical manual for selected algorithms implemented within the DAKOTA software. It is not intended as a comprehensive theoretical treatment, since a number of existing texts cover general optimization theory, statistical analysis, and other introductory topics. Rather, this manual is intended to summarize a set of DAKOTA-related research publications in the areas of surrogate-based optimization, uncertainty quantification, and optimization under uncertainty that provide the foundation for many of DAKOTA's iterative analysis capabilities.

99 GENERAL AND MISCELLANEOUS↗

DOE OSTI2014

Dakota, a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis version 6.0 theory manual

The Dakota (Design Analysis Kit for Optimization and Terascale Applications) toolkit provides a exible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quanti cation with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the Dakota toolkit provides a exible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a theoretical manual for selected algorithms implemented within the Dakota software. It is not intended as a comprehensive theoretical treatment, since a number of existing texts cover general optimization theory, statistical analysis, and other introductory topics. Rather, this manual is intended to summarize a set of Dakota-related research publications in the areas of surrogate-based optimization, uncertainty quanti cation, and optimization under uncertainty that provide the foundation for many of Dakota's iterative analysis capabilities.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2014

Dakota, a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis :

The Dakota (Design Analysis Kit for Optimization and Terascale Applications) toolkit provides a exible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quanti cation with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the Dakota toolkit provides a exible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a user's manual for the Dakota software and provides capability overviews and procedures for software execution, as well as a variety of example studies.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Dakota A Multilevel Parallel Object-Oriented Framework for Design Optimization Parameter Estimation Uncertainty Quantification and Sensitivity Analysis: Version 6.12 Theory Manual

The Dakota toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the Dakota toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a theoretical manual for selected algorithms implemented within the Dakota software. It is not intended as a comprehensive theoretical treatment, since a number of existing texts cover general optimization theory, statistical analysis, and other introductory topics. Rather, this manual is intended to summarize a set of Dakota-related research publications in the areas of surrogate-based optimization, uncertainty quantification, and optimization under uncertainty that provide the foundation for many of Dakota's iterative analysis capabilities.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Dakota, A Multilevel Parallel Object-Oriented Framework for Design Optimization Parameter Estimation Uncertainty Quantification and Sensitivity Analysis: Version 6.12 User's Manual

The Dakota toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the Dakota toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a user's manual for the Dakota software and provides capability overviews and procedures for software execution, as well as a variety of example studies.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Dakota A Multilevel Parallel Object-Oriented Framework for Design Optimization Parameter Estimation Uncertainty Quantification and Sensitivity Analysis (V.6.14) (Theory Manual)

The Dakota toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the Dakota toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a theoretical manual for selected algorithms implemented within the Dakota software. It is not intended as a comprehensive theoretical treatment, since a number of existing texts cover general optimization theory, statistical analysis, and other introductory topics. Rather, this manual is intended to summarize a set of Dakota-related research publications in the areas of surrogate-based optimization, uncertainty quantification, and optimization under uncertainty that provide the foundation for many of Dakota's iterative analysis capabilities.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Dakota A Multilevel Parallel Object-Oriented Framework for Design Optimization Parameter Estimation Uncertainty Quantification and Sensitivity Analysis (V.6.14) (User's Manual)

The Dakota toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the Dakota toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a users manual for the Dakota software and provides capability overviews and procedures for software execution, as well as a variety of example studies.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Dakota, A Multilevel Parallel Object-Oriented Framework for Design Optimization, Parameter Estimation, Uncertainty Quantification, and Sensitivity Analysis: Version 6.13 Theory Manual

The Dakota toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the Dakota toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a theoretical manual for selected algorithms implemented within the Dakota software. It is not intended as a comprehensive theoretical treatment, since a number of existing texts cover general optimization theory, statistical analysis, and other introductory topics. Rather, this manual is intended to summarize a set of Dakota-related research publications in the areas of surrogate-based optimization, uncertainty quantification, and optimization under uncertainty that provide the foundation for many of Dakota's iterative analysis capabilities.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Dakota, A Multilevel Parallel Object-Oriented Framework for Design Optimization, Parameter Estimation, Uncertainty Quantification, and Sensitivity Analysis: Version 6.13 User's Manual

The Dakota toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the Dakota toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a user’s manual for the Dakota software and provides capability overviews and procedures for software execution, as well as a variety of example studies.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Dakota, A Multilevel Parallel Object-Oriented Framework for Design Optimization, Parameter Estimation, Uncertainty Quantification, and Sensitivity Analysis: Version 6.15 User's Manual

The Dakota toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the Dakota toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Dakota, A Multilevel Parallel Object-Oriented Framework for Design Optimization, Parameter Estimation, Uncertainty Quantification, and Sensitivity Analysis: Theory Manual (V.6.15)

The Dakota toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the Dakota toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a theoretical manual for selected algorithms implemented within the Dakota software. It is not intended as a comprehensive theoretical treatment, since a number of existing texts cover general optimization theory, statistical analysis, and other introductory topics. Rather, this manual is intended to summarize a set of Dakota-related research publications in the areas of surrogate-based optimization, uncertainty quantification, and optimization under uncertainty that provide the foundation for many of Dakota's iterative analysis capabilities.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Dakota, A Multilevel Parallel Object-Oriented Framework for Design Optimization, Parameter Estimation, Uncertainty Quantification, and Sensitivity Analysis (V.6.16 User's Manual)

The Dakota toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the Dakota toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a user's manual for the Dakota software and provides capability overviews and procedures for software execution, as well as a variety of example studies.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Dakota, A Multilevel Parallel Object-Oriented Framework for Design Optimization, Parameter Estimation, Uncertainty Quantification, and Sensitivity Analysis: Version 6.16 Theory Manual

The Dakota toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the Dakota toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a theoretical manual for selected algorithms implemented within the Dakota software. It is not intended as a comprehensive theoretical treatment, since a number of existing texts cover general optimization theory, statistical analysis, and other introductory topics. Rather, this manual is intended to summarize a set of Dakota-related research publications in the areas of surrogate-based optimization, uncertainty quantification, and optimization under uncertainty that provide the foundation for many of Dakota’s iterative analysis capabilities.

97 MATHEMATICS AND COMPUTING↗