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Outer approximation for generalized convex mixed-integer nonlinear robust optimization problems

  • We consider nonlinear robust optimization problems with mixed-integer decisions as well as nonconvexities. In detail, we consider cases where objective and constraint functions can be nonsmooth and generalized convex, i.e., f°-quasiconvex or f°-pseudoconvex. We propose an algorithm for such robust optimization problems that does not require a certain structure of the adversarial problem but only requires that approximate worst cases are available. As a result, our algorithm finds a robust optimal solution up to a tolerance. Our method integrates a bundle method into an outer approximation approach where the bundle method is used for the arising continuous subproblems. We rely on methods from the literature, namely a bundle method for nonlinear and nonconvex robust optimization problems and outer approximation approaches for quasiconvex settings. Our contribution is to combine them to one convergent robust optimization method that can cope with inexactness of worst-case evaluations. Further, we propose the gas transport under uncertainties as a relevant application and demonstrate that generalized convexity is fulfilled for a type of a network structure.

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Author:Martina Kuchlbauer
Document Type:Preprint
Language:English
Date of Publication (online):2024/05/16
Release Date:2024/05/16
Subprojects:B06
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International