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3623. A Safe Approximation of Distributionally Robust Problems Depending on Univariate Indicator Functions
Invited abstract in session WB-4: Mixed Integer Nonlinear Programming and Nonconvex Optimization , stream MINLP.
Wednesday, 10:30-12:00Room: 1001 (building: 202)
Authors (first author is the speaker)
| 1. | Jan Rolfes
|
| Mathematics, Linköping University | |
| 2. | Jana Dienstbier
|
| Department of Data Science, Friedrich-Alexander University Erlangen-Nuremberg | |
| 3. | Frauke Liers
|
| Department Mathematik, FAU Erlangen-Nuremberg |
Abstract
Driven by an application from chromatography, we model an optimization problem with linear objective subject to robust constraints that depend on uncertain particle size distributions (psd).
The ambiguity set of our model can exploit information on moments as well as confidence sets. Moreover, we present a duality-based reformulation approach for distributionally robust problems, where the objective of the adverserial is allowed to depend on univariate indicator functions. This renders the problem nonlinear and nonconvex. In order to be able to reformulate the resulting semiinfinite constraints nevertheless, a safe approximation is presented that is realized by a discretized counterpart. Its reformulation leads to a mixed-integer linear problem that yields sufficient conditions for distributional robustness of the original problem. Furthermore, it is proven that with increasingly fine discretizations, the discretized reformulation converges to the original distributionally robust problem.
Computational results for the chromatographic setting show that the safe approximation yields robust solutions of high-quality within short time.
Keywords
- Robust Optimization
- Programming, Mixed-Integer
- Process Systems Engineering
Status: accepted
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