Framework for Mixed-Variable Optimization Under Uncertainty Using Surrogates and Statistical Selection

2004 ◽  
Author(s):  
Todd Sriver ◽  
James Chrissis
Keyword(s):  
Optimization Under Uncertainty ◽  
Statistical Selection ◽  
Mixed Variable

scholarly journals On quantitative stability in infinite-dimensional optimization under uncertainty

2021 ◽  
Author(s):  
M. Hoffhues ◽  
W. Römisch ◽  
T. M. Surowiec
Keyword(s):  
Stochastic Optimization ◽  
Constrained Optimization ◽  
Optimization Problems ◽  
Optimization Under Uncertainty ◽  
Optimal Solutions ◽  
Probability Metrics ◽  
Pde Constrained Optimization ◽  
Quantitative Stability ◽  
Infinite Dimensional ◽  
Optimal Value

AbstractThe vast majority of stochastic optimization problems require the approximation of the underlying probability measure, e.g., by sampling or using observations. It is therefore crucial to understand the dependence of the optimal value and optimal solutions on these approximations as the sample size increases or more data becomes available. Due to the weak convergence properties of sequences of probability measures, there is no guarantee that these quantities will exhibit favorable asymptotic properties. We consider a class of infinite-dimensional stochastic optimization problems inspired by recent work on PDE-constrained optimization as well as functional data analysis. For this class of problems, we provide both qualitative and quantitative stability results on the optimal value and optimal solutions. In both cases, we make use of the method of probability metrics. The optimal values are shown to be Lipschitz continuous with respect to a minimal information metric and consequently, under further regularity assumptions, with respect to certain Fortet-Mourier and Wasserstein metrics. We prove that even in the most favorable setting, the solutions are at best Hölder continuous with respect to changes in the underlying measure. The theoretical results are tested in the context of Monte Carlo approximation for a numerical example involving PDE-constrained optimization under uncertainty.

scholarly journals A density-matching approach for optimization under uncertainty

2016 ◽  
Vol 305 ◽  
pp. 562-578 ◽  
Author(s):  
Pranay Seshadri ◽  
Paul Constantine ◽  
Gianluca Iaccarino ◽  
Geoffrey Parks
Keyword(s):  
Optimization Under Uncertainty

Developing Selection Skills in Introductory Statistics

1991 ◽  
Vol 18 (4) ◽  
pp. 219-222 ◽  
Author(s):  
Mark E. Ware ◽  
Jeffrey D. Chastain
Keyword(s):  
Statistical Tests ◽  
Teaching Strategy ◽  
Analysis Of Covariance ◽  
Introductory Statistics ◽  
Statistics Analysis ◽  
Pedagogical Strategies ◽  
Personality Variables ◽  
Statistical Selection ◽  
Confounding Variables

We assessed the effectiveness of a teaching strategy emphasizing the use of different statistical tests (i. e., selection skills) in introductory statistics. Subjects were 127 undergraduates enrolled in introductory statistics classes that did or did not emphasize selection skills and students not enrolled in statistics. Analysis of covariance revealed that emphasizing statistical selection skills produced the highest selection scores. Analyses also evaluated relevant confounding variables. Although students' selection skills can be increased when the instructor emphasizes those skills in handouts, lectures, and examinations, a challenge remains to identify other relevant skilb, develop alternative pedagogical strategies, and discover relevant personality variables that facilitate learning in statistics classes.

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