We focus on a novel assay utilizing this approach, called selective 2'-hydroxyl acylation analyzed by primer extension sequencing (SHAPE-Seq), that can be used to characterize RNA secondary and tertiary structure. We describe a fully automated data analysis pipeline for SHAPE-Seq analysis that includes read processing, mapping, and structural inference based on a model of the experiment. Our methods rely on the solution of a series of convex optimization problems for which we develop efficient and effective numerical algorithms.