Convergence Properties of the Nelder--Mead Simplex Method in Low Dimensions
SIAM Journal on Optimization
A convergent variant of the Nelder-Mead algorithm
Journal of Optimization Theory and Applications
A Novel Sampling Approach to Combinatorial Optimization Under Uncertainty
Computational Optimization and Applications
Analysis of Generalized Pattern Searches
SIAM Journal on Optimization
Multidirectional search: a direct search algorithm for parallel machines
Multidirectional search: a direct search algorithm for parallel machines
Frames and Grids in Unconstrained and Linearly Constrained Optimization: A Nonsmooth Approach
SIAM Journal on Optimization
Introduction: Optimization and Risk Modelling
Computational Optimization and Applications
Grid Restrained Nelder-Mead Algorithm
Computational Optimization and Applications
Multi-element probabilistic collocation method in high dimensions
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Implementing the Nelder-Mead simplex algorithm with adaptive parameters
Computational Optimization and Applications
SIAM Journal on Scientific Computing
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The Simplex Stochastic Collocation (SSC) method is an efficient algorithm for uncertainty quantification (UQ) in computational problems with random inputs. In this work, we show how its formulation based on simplex tessellation, high degree polynomial interpolation and adaptive refinements can be employed in problems involving optimization under uncertainty. The optimization approach used is the Nelder-Mead algorithm (NM), also known as Downhill Simplex Method. The resulting SSC/NM method, called Simplex2, is based on (i) a coupled stopping criterion and (ii) the use of an high-degree polynomial interpolation in the optimization space for accelerating some NM operators. Numerical results show that this method is very efficient for mono-objective optimization and minimizes the global number of deterministic evaluations to determine a robust design. This method is applied to some analytical test cases and a realistic problem of robust optimization of a multi-component airfoil.