Bernhard D, Liers F, Stingl M (2025)
Publication Language: English
Publication Status: Submitted
Publication Type: Unpublished / Preprint
Future Publication Type: Journal article
Publication year: 2025
URI: https://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/564
Typically, probability distributions that generate uncertain parameters are uncertain themselves or even unknown. As a remedy, distributional robustness determines optimized decisions that are protected in a robust fashion against all probability distributions in some appropriately chosen ambiguity set. In this work, we consider robust joint chance-constrained optimization problems and focus on discrete probability distributions. Many methods for this kind of problems study convex or even linear constraint functions. In contrast, we introduce a practically efficient scenario-based bundle method without convexity assumptions on the constraint functions. We start by deriving an approximation problem to the original robust chance-constrained version by using smoothing and penalization techniques that build on our former work on chance-constrained optimization. Our
convergence results with respect to the smoothing approximation and well-known results for penalty approximations suggest replacing the original problem with the approximation problem for large smoothing and penalty parameters. Our scenario-based bundle method starts by solving the approximation problem with a bundle method, and then uses the bundle solution to decide which scenarios to include in a scenario-expanded formulation. This formulation is a standard nonlinear optimization problem. In our numerical experiments we demonstrate the efficiency of our approach on real-world gas transport problems with uncertain demands. Comparing our results to the classical robust reformulations for ambiguity sets consisting of confidence intervals and Wasserstein balls, we observe that the scenario-based bundle method often outperforms solving the classical reformulation directly.
APA:
Bernhard, D., Liers, F., & Stingl, M. (2024). Robust chance-constrained optimization with discrete distributions. (Unpublished, Submitted).
MLA:
Bernhard, Daniela, Frauke Liers, and Michael Stingl. Robust chance-constrained optimization with discrete distributions. Unpublished, Submitted. 2024.
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