192. A Positive Semidefinite Safe Approximation of Multivariate Distributionally Robust Constraints Determined by Simple Functions
Invited abstract in session MC-11: Advances in conic optimization, stream Conic Optimization.
Monday, 14:00-16:00Room: B100/5017
Authors (first author is the speaker)
| 1. | Jan Rolfes
|
| Mathematics, Linköping University | |
| 2. | Jana Dienstbier
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| Department of Data Science, Friedrich-Alexander University Erlangen-Nuremberg | |
| 3. | Frauke Liers
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| Department Mathematik, FAU Erlangen-Nuremberg |
Abstract
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 can at least in part be overcome. 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.
Keywords
- Distributionally robust optimization
- Nonlinear mixed integer optimization
- Optimization under uncertainty
Status: accepted
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