A Multilevel Stochastic Collocation Algorithm for Optimization of PDEs with Uncertain Coefficients

A Trust-Region Algorithm with Adaptive Stochastic Collocation for PDE Optimization under Uncertainty

(2013) D. P. Kouri et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

A stochastic collocation method for the second order wave equation with a discontinuous random speed

(2012) Mohammad Motamed et al.   NUMERISCHE MATHEMATIK

Properties of a class of multilevel optimization algorithms for equality-constrained problems

(2012) Stephen G. Nash   OPTIMIZATION METHODS & SOFTWARE

On the Use of Stochastic Hessian Information in Optimization Methods for Machine Learning

(2011) Richard H. Byrd et al.   SIAM JOURNAL ON OPTIMIZATION

A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data

(2010) Ivo Babuška et al.   SIAM REVIEW

Analysis and implementation issues for the numerical approximation of parabolic equations with random coefficients

(2009) F. Nobile et al.   INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING

On the Convergence of Recursive Trust-Region Methods for Multiscale Nonlinear Optimization and Applications to Nonlinear Mechanics

(2009) Christian Gross et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

A Line Search Multigrid Method for Large-Scale Nonlinear Optimization

(2009) Zaiwen Wen et al.   SIAM JOURNAL ON OPTIMIZATION

Multigrid Methods and Sparse-Grid Collocation Techniques for Parabolic Optimal Control Problems with Random Coefficients

(2009) A. Borzì et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Multigrid Methods for PDE Optimization

(2009) Alfio Borzì et al.   SIAM REVIEW

Multigrid optimization methods for linear and bilinear elliptic optimal control problems

(2008) Michelle Vallejos et al.   COMPUTING

An Anisotropic Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data

(2008) F. Nobile et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data

(2008) F. Nobile et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Recursive Trust-Region Methods for Multiscale Nonlinear Optimization

(2008) Serge Gratton et al.   SIAM JOURNAL ON OPTIMIZATION