Pareto robust optimization on Euclidean vector spaces

Author:

Adelhütte DennisORCID,Biefel ChristianORCID,Kuchlbauer MartinaORCID,Rolfes JanORCID

Abstract

AbstractPareto efficiency for robust linear programs was introduced by Iancu and Trichakis in [Manage Sci 60(1):130–147, 9]. We generalize their approach and theoretical results to robust optimization problems in Euclidean spaces with affine uncertainty. Additionally, we demonstrate the value of this approach in an exemplary manner in the area of robust semidefinite programming (SDP). In particular, we prove that computing a Pareto robustly optimal solution for a robust SDP is tractable and illustrate the benefit of such solutions at the example of the maximal eigenvalue problem. Furthermore, we modify the famous algorithm of Goemans and Williamson [Assoc Comput Mach 42(6):1115–1145, 8] in order to compute cuts for the robust max-cut problem that yield an improved approximation guarantee in non-worst-case scenarios.

Funder

Deutsche Forschungsgemeinschaft

HORIZON EUROPE Marie Sklodowska-Curie Actions

Friedrich-Alexander-Universität Erlangen-Nürnberg

Publisher

Springer Science and Business Media LLC

Subject

Control and Optimization,Business, Management and Accounting (miscellaneous)

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