Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
A maximum entropy approach to natural language processing
Computational Linguistics
Filters, Random Fields and Maximum Entropy (FRAME): Towards a Unified Theory for Texture Modeling
International Journal of Computer Vision
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
SIAM Journal on Scientific Computing
On the Convergence of Pattern Search Algorithms
SIAM Journal on Optimization
Pattern Search Algorithms for Bound Constrained Minimization
SIAM Journal on Optimization
Pattern Search Methods for Linearly Constrained Minimization
SIAM Journal on Optimization
Analysis of Generalized Pattern Searches
SIAM Journal on Optimization
A Pattern Search Filter Method for Nonlinear Programming without Derivatives
SIAM Journal on Optimization
High-Order Collocation Methods for Differential Equations with Random Inputs
SIAM Journal on Scientific Computing
Algorithm 847: Spinterp: piecewise multilinear hierarchical sparse grid interpolation in MATLAB
ACM Transactions on Mathematical Software (TOMS)
Mesh Adaptive Direct Search Algorithms for Constrained Optimization
SIAM Journal on Optimization
Sparse grid collocation schemes for stochastic natural convection problems
Journal of Computational Physics
A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data
SIAM Journal on Numerical Analysis
Journal of Computational Physics
A Progressive Barrier for Derivative-Free Nonlinear Programming
SIAM Journal on Optimization
OrthoMADS: A Deterministic MADS Instance with Orthogonal Directions
SIAM Journal on Optimization
Accelerating evolutionary algorithms with Gaussian process fitness function models
IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews
Free Pattern Search for global optimization
Applied Soft Computing
A simplex-based numerical framework for simple and efficient robust design optimization
Computational Optimization and Applications
Fluid---structure interaction simulation of pulsatile ventricular assist devices
Computational Mechanics
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Recent advances in coupling novel optimization methods to large-scale computing problems have opened the door to tackling a diverse set of physically realistic engineering design problems. A large computational overhead is associated with computing the cost function for most practical problems involving complex physical phenomena. Such problems are also plagued with uncertainties in a diverse set of parameters. We present a novel stochastic derivative-free optimization approach for tackling such problems. Our method extends the previously developed surrogate management framework (SMF) to allow for uncertainties in both simulation parameters and design variables. The stochastic collocation scheme is employed for stochastic variables whereas Kriging based surrogate functions are employed for the cost function. This approach is tested on four numerical optimization problems and is shown to have significant improvement in efficiency over traditional Monte-Carlo schemes. Problems with multiple probabilistic constraints are also discussed.