Dienstbier J, Liers F, Rolfes J (2024)
Publication Language: English
Publication Status: Submitted
Publication Type: Unpublished / Preprint
Future Publication Type: Other publication type
Publication year: 2024
URI: https://arxiv.org/abs/2301.11185
In this work, we present algorithmically tractable safe approxima-
tions of distributionally robust optimization (DRO) problems. The considered
ambiguity sets can exploit information on moments as well as confidence sets.
Typically, reformulation approaches using duality theory need to make strong
assumptions on the structure of the underlying constraints, such as convexity
in the decisions or concavity in the uncertainty. In contrast, here we present a
duality-based reformulation approach for DRO problems, where the objective of
the adverserial is allowed to depend on univariate indicator functions. This ren-
ders the problem nonlinear and nonconvex. In order to be able to reformulate
the semiinfinite constraints nevertheless, an exact reformulation is presented
that is approximated by a discretized counterpart. The approximation is re-
alized as 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. The approach is made concrete
for a challenging, fundamental task in particle separation that appears in
material design. Computational results for realistic settings show that the safe
approximation yields robust solutions of high-quality and can be computed
within short time
APA:
Dienstbier, J., Liers, F., & Rolfes, J. (2024). A Safe Approximation Based on Mixed-Integer Optimization for Non-Convex Distributional Robustness Governed by Univariate Indicator Functions. (Unpublished, Submitted).
MLA:
Dienstbier, Jana, Frauke Liers, and Jan Rolfes. A Safe Approximation Based on Mixed-Integer Optimization for Non-Convex Distributional Robustness Governed by Univariate Indicator Functions. Unpublished, Submitted. 2024.
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