Dienstbier J, Liers F, Rolfes J (2024)
Publication Status: Submitted
Publication Type: Unpublished / Preprint
Future Publication Type: Journal article
Publication year: 2024
URI: https://arxiv.org/abs/2310.05612
DOI: 10.48550/arXiv.2310.05612
Single-level reformulations of (non-convex) distributionally robust
optimization (DRO) problems are often intractable, as they contain semiinfinite
dual constraints. Based on such a semiinfinite reformulation, we present a
safe approximation, that allows for the computation of feasible solutions for
DROs that depend on nonconvex multivariate simple functions. Moreover,
the approximation allows to address ambiguity sets that can incorporate
information on moments as well as confidence sets. The typical strong assumptions
on the structure of the underlying constraints, such as convexity in the
decisions or concavity in the uncertainty found in the literature were, at
least in part, recently overcome in [10]. We start from the duality-based
reformulation approach in [10] that can be applied for DRO constraints based
on simple functions that are univariate in the uncertainty parameters. We
significantly extend their approach to multivariate simple functions which leads
to a considerably wider applicability of the proposed reformulation approach.
In order to achieve algorithmic tractability, the presented safe approximation is
then realized by a discretized counterpart for the semiinfinite dual constraints.
The approximation leads to a computationally tractable mixed-integer positive
semidefinite problem for which state-of-the-art software implementations are
readily available. The tractable safe approximation provides sufficient conditions
for distributional robustness of the original problem, i.e., obtained solutions
are provably robust.
APA:
Dienstbier, J., Liers, F., & Rolfes, J. (2024). A Positive Semidefinite Safe Approximation of Multivariate Distributionally Robust Constraints Determined by Simple Functions. (Unpublished, Submitted).
MLA:
Dienstbier, Jana, Frauke Liers, and Jan Rolfes. A Positive Semidefinite Safe Approximation of Multivariate Distributionally Robust Constraints Determined by Simple Functions. Unpublished, Submitted. 2024.
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