  The generation of feasible adversarial examples is necessary for properly
assessing models that work in constrained feature space. However, it remains a
challenging task to enforce constraints into attacks that were designed for
computer vision. We propose a unified framework to generate feasible
adversarial examples that satisfy given domain constraints. Our framework can
handle both linear and non-linear constraints. We instantiate our framework
into two algorithms: a gradient-based attack that introduces constraints in the
loss function to maximize, and a multi-objective search algorithm that aims for
misclassification, perturbation minimization, and constraint satisfaction. We
show that our approach is effective in four different domains, with a success
rate of up to 100%, where state-of-the-art attacks fail to generate a single
feasible example. In addition to adversarial retraining, we propose to
introduce engineered non-convex constraints to improve model adversarial
robustness. We demonstrate that this new defense is as effective as adversarial
retraining. Our framework forms the starting point for research on constrained
adversarial attacks and provides relevant baselines and datasets that future
research can exploit.
