This paper presents a scheme for dual robust control of batch processes under parametric uncertainty. The dual-control paradigm arises in the context of adaptive control. A trade-off should be decided between the control actions that (robustly) optimize the plant performance and between those that excite the plant such that unknown plant model parameters can be learned precisely enough to increase the robust performance of the plant. Some recently proposed approaches can be used to tackle this problem; however, this will be done at measurements the price of conservativeness or significant computational burden. In order to increase computational efficiency, we propose a scheme that uses parametrized conditions of optimality in the adaptive predictive-control fashion. The dual features of the controller are incorporated through a scenario-based (multi-stage) approach, which allows for modeling of the adaptive robust decision problem and for projecting this decision into predictions of the controller. The proposed approach is illustrated on a case study from membrane filtration.