Scenarios and policy aggregation in optimization under uncertainty
Mathematics of Operations Research
Three-dimensional perfectly matched layer for the absorption of electromagnetic waves
Journal of Computational Physics
Mathematics of Operations Research
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
GloptiPoly: Global optimization over polynomials with Matlab and SeDuMi
ACM Transactions on Mathematical Software (TOMS)
Tractable Approximations to Robust Conic Optimization Problems
Mathematical Programming: Series A and B
An approximation technique for robust nonlinear optimization
Mathematical Programming: Series A and B
Computational complexity of stochastic programming problems
Mathematical Programming: Series A and B
Concepts and Applications of Finite Element Analysis
Concepts and Applications of Finite Element Analysis
Nonconvex Robust Optimization for Problems with Constraints
INFORMS Journal on Computing
Robust optimization with simulated annealing
Journal of Global Optimization
Min-max and robust polynomial optimization
Journal of Global Optimization
Robust Optimization in Simulation: Taguchi and Krige Combined
INFORMS Journal on Computing
A distributed agent-based approach for simulation-based optimization
Advanced Engineering Informatics
Adaptive probabilistic branch and bound for level set approximation
Proceedings of the Winter Simulation Conference
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In engineering design, an optimized solution often turns out to be suboptimal when errors are encountered. Although the theory of robust convex optimization has taken significant strides over the past decade, all approaches fail if the underlying cost function is not explicitly given; it is even worse if the cost function is nonconvex. In this work, we present a robust optimization method that is suited for unconstrained problems with a nonconvex cost function as well as for problems based on simulations, such as large partial differential equations (PDE) solver, response surface, and Kriging metamodels. Moreover, this technique can be employed for most real-world problems because it operates directly on the response surface and does not assume any specific structure of the problem. We present this algorithm along with the application to an actual engineering problem in electromagnetic multiple scattering of aperiodically arranged dielectrics, relevant to nanophotonic design. The corresponding objective function is highly nonconvex and resides in a 100-dimensional design space. Starting from an “optimized” design, we report a robust solution with a significantly lower worst-case cost, while maintaining optimality. We further generalize this algorithm to address a nonconvex optimization problem under both implementation errors and parameter uncertainties.