Dakota Reference Manual
Version 6.4
LargeScale Engineering Optimization and Uncertainty Analysis

Specify which MPP search option to use
This keyword is related to the topics:
Alias: none
Argument(s): none
Default: No MPP search (MV method)
Required/Optional  Description of Group  Dakota Keyword  Dakota Keyword Description  

Required (Choose One)  Group 1  x_taylor_mean  Form Taylor series approximation in "xspace" at variable means  
u_taylor_mean  Form Taylor series approximation in "uspace" at variable means  
x_taylor_mpp  Xspace Taylor series approximation with iterative updates  
u_taylor_mpp  Uspace Taylor series approximation with iterative updates  
x_two_point  Predict MPP using Twopoint Adaptive Nonlinear Approximation in "xspace"  
u_two_point  Predict MPP using Twopoint Adaptive Nonlinear Approximation in "uspace"  
no_approx  Perform MPP search on original response functions (use no approximation)  
Optional (Choose One)  Group 2  sqp  Uses a sequential quadratic programming method for underlying optimization  
nip  Uses a nonlinear interior point method for underlying optimization  
Optional  integration  Integration approach 
The x_taylor_mean
MPP search option performs a single Taylor series approximation in the space of the original uncertain variables ("xspace") centered at the uncertain variable means, searches for the MPP for each response/probability level using this approximation, and performs a validation response evaluation at each predicted MPP. This option is commonly known as the Advanced Mean Value (AMV) method. The u_taylor_mean
option is identical to the x_taylor_mean
option, except that the approximation is performed in uspace. The x_taylor_mpp
approach starts with an xspace Taylor series at the uncertain variable means, but iteratively updates the Taylor series approximation at each MPP prediction until the MPP converges. This option is commonly known as the AMV+ method. The u_taylor_mpp
option is identical to the x_taylor_mpp
option, except that all approximations are performed in uspace. The order of the Taylorseries approximation is determined by the corresponding responses
specification and may be first or secondorder. If secondorder (methods named and in [20]), the series may employ analytic, finite difference, or quasi Hessians (BFGS or SR1). The x_two_point
MPP search option uses an xspace Taylor series approximation at the uncertain variable means for the initial MPP prediction, then utilizes the Twopoint Adaptive Nonlinear Approximation (TANA) outlined in[91] for all subsequent MPP predictions. The u_two_point
approach is identical to x_two_point
, but all the approximations are performed in uspace. The x_taylor_mpp
and u_taylor_mpp
, x_two_point
and u_two_point
approaches utilize the max_iterations
and convergence_tolerance
method independent controls to control the convergence of the MPP iterations (the maximum number of MPP iterations per level is limited by max_iterations
, and the MPP iterations are considered converged when < convergence_tolerance
). And, finally, the no_approx
option performs the MPP search on the original response functions without the use of any approximations. The optimization algorithm used to perform these MPP searches can be selected to be either sequential quadratic programming (uses the npsol_sqp
optimizer) or nonlinear interior point (uses the optpp_q_newton
optimizer) algorithms using the sqp
or nip
keywords.
In addition to the MPP search specifications, one may select among different integration approaches for computing probabilities at the MPP by using the integration
keyword followed by either first_order
or second_order
. Secondorder integration employs the formulation of[49] (the approach of[12] and the correction of[50] are also implemented, but are not active). Combining the no_approx
option of the MPP search with first and secondorder integrations results in the traditional first and secondorder reliability methods (FORM and SORM). These integration approximations may be subsequently refined using importance sampling. The refinement
specification allows the seletion of basic importance sampling (import
), adaptive importance sampling (adapt_import
), or multimodal adaptive importance sampling (mm_adapt_import
), along with the specification of number of samples (samples
) and random seed (seed
). Additional details on these methods are available in[22] and[20] and in the Uncertainty Quantification Capabilities chapter of the Users Manual [5].