Moment Relaxations for Data-Driven Wasserstein Distributionally Robust Optimization

2025/05/25 by Zhang, Shixuan, Zhong, Suhan
#FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2505.19278

Abstract

We propose moment relaxations for data-driven Wasserstein distributionally robust optimization problems. Conditions are identified to ensure asymptotic consistency of such relaxations for both single-stage and two-stage problems, together with examples that illustrate their necessity. Numerical experiments are also included to illustrate the proposed relaxations.

Citations

• Spurious local minima in nonconvex sum-of-squares optimization
• Distributionally Robust Optimization with Polynomial Robust Constraints
• Two-Stage Distributionally Robust Conic Linear Programming over 1-Wasserstein Balls
• On Distributionally Robust Multistage Convex Optimization: Data-driven Models and Performance
• JuMP 1.0: Recent improvements to a modeling language for mathematical optimization
• Statistical Analysis of Wasserstein Distributionally Robust Estimators
• Distributionally Robust Optimization with Moment Ambiguity Sets
• Finite-Sample Guarantees for Wasserstein Distributionally Robust Optimization: Breaking the Curse of Dimensionality
• Sparse PSD approximation of the PSD cone
• On the Burer-Monteiro method for general semidefinite programs
• Distributionally robust optimization with polynomial densities: theory,\n models and algorithms
• DSOS and SDSOS Optimization: More Tractable Alternatives to Sum of\n Squares and Semidefinite Optimization
• Decomposition Algorithm for Distributionally Robust Optimization using Wasserstein Metric
• Distributionally Robust Stochastic Optimization with Wasserstein Distance
• Distributionally Robust Stochastic Optimization with Wasserstein Distance
• Data-driven Distributionally Robust Optimization Using the Wasserstein\n Metric: Performance Guarantees and Tractable Reformulations
• Data-driven distributionally robust optimization using the Wasserstein metric: performance guarantees and tractable reformulations
• On the rate of convergence in Wasserstein distance of the empirical measure
• Strong duality in conic linear programming: facial reduction and extended duals
• Polynomials non-negative on strips and half-strips
• A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization

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• Data-driven Distributionally Robust Optimization Using the Wasserstein\n Metric: Performance Guarantees and Tractable Reformulations
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