The paper derives tractable single-level reformulations of distributionally robust shape and topology optimization for Wasserstein, moment, and CVaR ambiguity sets, and demonstrates them numerically.
Sinkhorn Distributionally Robust Optimization
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abstract
We study distributionally robust optimization with Sinkhorn distance -- a variant of Wasserstein distance based on entropic regularization. We derive a convex programming dual reformulation for general nominal distributions, transport costs, and loss functions. To solve the dual reformulation, we develop a stochastic mirror descent algorithm with biased subgradient estimators and derive its computational complexity guarantees. Finally, we provide numerical examples using synthetic and real data to demonstrate its superior performance.
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Distributionally Robust Shape and Topology Optimization
The paper derives tractable single-level reformulations of distributionally robust shape and topology optimization for Wasserstein, moment, and CVaR ambiguity sets, and demonstrates them numerically.