Nonlinear multigrid methods for total variation image denoising

2004 ◽  
Vol 7 (3-4) ◽  
pp. 199-206 ◽  
Author(s):  
Claudia Frohn-Schauf ◽  
Stefan Henn ◽  
Kristian Witsch
Keyword(s):  
Image Denoising ◽  
Total Variation ◽  
Multigrid Methods ◽  
Nonlinear Multigrid ◽  
Nonlinear Multigrid Methods

Monotonicity and Active Set Strategies in Probabilistic Design Optimization

2005 ◽  
Author(s):  
Kuei-Yuan Chan ◽  
Steven J. Skerlos ◽  
Panos Y. Papalambros
Keyword(s):  
Design Optimization ◽  
Computational Cost ◽  
Inequality Constraints ◽  
Probabilistic Constraints ◽  
Programming Algorithm ◽  
Probabilistic Design ◽  
Active Set ◽  
Probability Metrics ◽  
Active Set Strategies ◽  
Monotonicity Analysis

Probabilistic design optimization addresses the presence of uncertainty in design problems. Extensive studies on Reliability-Based Design Optimization (RBDO), i.e., problems with random variables and probabilistic constraints, have focused on improving computational efficiency of estimating values for the probabilistic functions. In the presence of many probabilistic inequality constraints, computational costs can be reduced if probabilistic values are computed only for constraints that are known to be active or likely active. This article presents an extension of monotonicity analysis concepts from deterministic problems to probabilistic ones, based on the fact that several probability metrics are monotonic transformations. These concepts can be used to construct active set strategies that reduce the computational cost associated with handling inequality constraints, similarly to the deterministic case. Such a strategy is presented as part of a sequential linear programming algorithm along with a numerical example.

Monotonicity and Active Set Strategies in Probabilistic Design Optimization

2006 ◽  
Vol 128 (4) ◽  
pp. 893-900 ◽  
Author(s):  
Kuei-Yuan Chan ◽  
Steven Skerlos ◽  
Panos Y. Papalambros
Keyword(s):  
Design Optimization ◽  
Computational Cost ◽  
Inequality Constraints ◽  
Probabilistic Constraints ◽  
Programming Algorithm ◽  
Probabilistic Design ◽  
Active Set ◽  
Probability Metrics ◽  
Active Set Strategies ◽  
Monotonicity Analysis

Probabilistic design optimization addresses the presence of uncertainty in design problems. Extensive studies on reliability-based design optimization, i.e., problems with random variables and probabilistic constraints, have focused on improving computational efficiency of estimating values for the probabilistic functions. In the presence of many probabilistic inequality constraints, computational costs can be reduced if probabilistic values are computed only for constraints that are known to be active or likely active. This article presents an extension of monotonicity analysis concepts from deterministic problems to probabilistic ones, based on the fact that several probability metrics are monotonic transformations. These concepts can be used to construct active set strategies that reduce the computational cost associated with handling inequality constraints, similarly to the deterministic case. Such a strategy is presented as part of a sequential linear programming algorithm along with numerical examples.

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