Qiao Yi Wang – Optimization Online

Asymptotic Consistency of Data-Driven Distributionally Robust Optimization via Reference-Distribution Convergence and Ambiguity-Set Shrinkage

Published: 2026/04/15, Updated: 2026/05/07

Robust Optimization, Stochastic Programming Ambiguity-set shrinkage, data-driven optimization, distributionally robust optimization, Painlevé-Kuratowski convergence, Statistical consistency

We study asymptotic consistency of data-driven distributionally robust optimization with shrinking ambiguity sets. The analysis separates reference-distribution convergence from ambiguity-set shrinkage on a prescribed test-function class. Under compactness and continuity assumptions, this yields uniform convergence of robust objectives, optimal-value convergence, and outer convergence of minimizers. For constrained DRO, the same mechanism gives uniform convergence of … Read more

KDE Robust Satisficing for Optimal Load Shedding Under Renewable Uncertainty

Published: 2026/03/31, Updated: 2026/04/01

Applications - Science and Engineering, Energy, Robust Optimization higher-moment coherent risk, kernel density estimation, Optimal load shedding, renewable uncertainty, robust-satisficing

Abstract—Renewable-driven direct-current optimal load shedding (DC-OLS) requires a model that is interpretable to operators, data driven under continuous forecast errors, sensitive to severe security failures, and computationally tractable. This paper develops a budgeted KDE-ϕ-HMCR-RS-OLS framework for that purpose. Robust satisficing (RS) replaces ambiguity-radius tuning with an admissible shedding budget. A one-dimensional KDE reference family with … Read more

Context-Aware Cluster-Based Multi-Uncertainty-Set Distributionally Robust Chance-Constrained DC Optimal Power Flow

Published: 2026/03/25, Updated: 2026/04/01

Qiao Yi Wang

Wei Liu

Bo Yu

Applications - Science and Engineering, Energy, Robust Optimization chance constraints, clustering, distributionally robust optimization, optimal power flow, renewable energy, wasserstein ambiguity

This paper proposes a context-aware multi-uncertainty-set distributionally robust chance-constrained DC optimal power flow model. Meteorological features are projected to partition the non-convex error support into a context-dependent decomposition of conditional local ambiguity sets, with conditional weights inferred via kernel regression. The minimax problem is reformulated into a finite-dimensional second-order cone program with proven asymptotic consistency. … Read more