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

We consider mixed-integer nonlinear robust optimization problems with nonconvexities. In detail, the functions can be nonsmooth and generalized convex, i.e., f degrees-quasiconvex or f degrees-pseudoconvex. We propose a robust optimization method that requires no certain structure of the adversarial problem, but only approximate worst-case evaluations. The method integrates a bundle method, for continuous subproblems, into an outer approximation approach. We prove that our algorithm converges and finds an approximately robust optimal solution and propose robust gas transport as a suitable application.