Gradual itemsets of the form "the more/less A, the more/less B" summarize data through the description of their internal tendencies, identified as correlation between attribute values. This paper proposes to enrich such gradual itemsets by taking into account an acceleration effect, leading to a new type of gradual itemset of the form "the more/less A increases, the more quickly B increases". It proposes an interpretation as convexity constraint imposed on the relation between A and B and a formalization of these accelerated gradual itemsets, as well as evaluation criteria. It illustrates the relevance of the proposed approach on real data.