Quantitative Stability Analysis for Distributionally Robust Optimization with Moment Constraints

DOI10.1137/15M1038529zbMath1346.90650MaRDI QIDQ2821799

Jie Zhang, Huifu Xu, Li-wei Zhang

Publication date: 23 September 2016

Published in: SIAM Journal on Optimization (Search for Journal in Brave)

zbMATH Keywords

distributionally robust optimizationquantitative stability analysisHölder continuity of the optimal value functionmoment conditions with cone constraintsouter semicontinuity of the set of optimal solutions

Mathematics Subject Classification ID

Sensitivity, stability, parametric optimization (90C31) Stochastic programming (90C15)

Related Items

A smooth approximation approach for optimization with probabilistic constraints based on sigmoid function ⋮ Distributionally robust optimization with matrix moment constraints: Lagrange duality and cutting plane methods ⋮ Stability of minimization problems and the error bound condition ⋮ Frameworks and results in distributionally robust optimization ⋮ Distributionally Robust Optimization Under a Decision-Dependent Ambiguity Set with Applications to Machine Scheduling and Humanitarian Logistics ⋮ Quantitative analysis for a class of two-stage stochastic linear variational inequality problems ⋮ Distributionally robust optimization under endogenous uncertainty with an application in retrofitting planning ⋮ Distributionally robust equilibrium for continuous games: Nash and Stackelberg models ⋮ A modified exchange algorithm for distributional robust optimization and applications in risk management ⋮ Diametrical risk minimization: theory and computations ⋮ A distributionally robust optimization approach for two-stage facility location problems ⋮ Pure characteristics demand models and distributionally robust mathematical programs with stochastic complementarity constraints ⋮ On distributionally robust optimization problems with \(k\)-th order stochastic dominance constraints induced by full random quadratic recourse ⋮ Stability Analysis of Optimization Problems with $k$th order stochastic and distributionally robust dominance constraints induced by full random recourse ⋮ Distributionally robust chance constrained optimization for economic dispatch in renewable energy integrated systems ⋮ Distributionally robust facility location problem under decision-dependent stochastic demand ⋮ Quantitative Stability of Two-Stage Linear Second-Order Conic Stochastic Programs with Full Random Recourse ⋮ Discrete Approximation and Quantification in Distributionally Robust Optimization ⋮ Quantitative stability of two-stage distributionally robust risk optimization problem with full random linear semi-definite recourse ⋮ Quantitative Stability Analysis for Distributionally Robust Optimization with Moment Constraints ⋮ Lopsided convergence: an extension and its quantification ⋮ Quantitative Stability Analysis of Two-Stage Stochastic Linear Programs with Full Random Recourse ⋮ Quantitative Stability and Empirical Approximation of Risk-Averse Models Induced by Two-Stage Stochastic Programs with Full Random Recourse ⋮ Bilevel Linear Optimization Under Uncertainty ⋮ Distributionally robust multi-period location-allocation with multiple resources and capacity levels in humanitarian logistics ⋮ Robustness of stochastic programs with endogenous randomness via contamination ⋮ Variational Theory for Optimization under Stochastic Ambiguity ⋮ Distributionally robust optimization with moment ambiguity sets ⋮ Quantitative stability analysis for minimax distributionally robust risk optimization

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Distributionally robust optimization with matrix moment constraints: Lagrange duality and cutting plane methods
• Applying the minimax criterion in stochastic recourse programs
• Data-driven distributionally robust optimization using the Wasserstein metric: performance guarantees and tractable reformulations
• Algorithms for the solution of stochastic dynamic minimax problems
• Data-driven risk-averse stochastic optimization with Wasserstein metric
• Convergence Analysis for Distributionally Robust Optimization and Equilibrium Problems
• Quantitative Stability Analysis for Distributionally Robust Optimization with Moment Constraints
• Multistage Stochastic Optimization
• Uncertainties in minimax stochastic programs
• Lectures on Stochastic Programming
• The Theory of Moral Hazard and Unobservable Behaviour: Part I
• Approximations for Probability Distributions and Stochastic Optimization Problems
• On Choosing and Bounding Probability Metrics
• A scenario aggregation algorithm for the solution of stochastic dynamic minimax problems
• A Cutting Surface Algorithm for Semi-Infinite Convex Programming with an Application to Moment Robust Optimization
• Ambiguity in portfolio selection
• Measure Theory and Probability Theory
• Minimax Theorems