We develop an algorithm for minimax problems that arise in robust optimization in the absence of objective function derivatives. The algorithm utilizes an extension of methods for inexact outer approximation in sampling a potentially infinite-cardinality uncertainty set. Clarke stationarity of the algorithm output is established alongside desirable features of the model-based trust-region subproblems encountered. We demonstrate the practical benefits of the algorithm on a new class of test problems.
Currently available as a preprint at Mathematics and Computer Science (MCS) Division of Argonne National Laboratory, 9700 South Cass Avenue, Lemont, Illinois 60439. Preprint ANL/MCS-P9004-1017, October 2017.