We present IQR, a system that demonstrates optimization based interactive relaxations for queries that return an empty answer. Given an empty answer, IQR dynamically suggests one relaxation of the original query conditions at a time to the user, based on certain optimization objectives, and the user responds by either accepting or declining the relaxation, until the user arrives at a non-empty answer, or a non-empty answer is impossible to achieve with any further relaxations. The relaxation suggestions hinge on a probabilistic framework that takes into account the probability of the user accepting a suggested relaxation, as well as how much that relaxation serves towards the optimization objective. IQR accepts a wide variety of optimization objectives - user centric objectives, such as, minimizing the number of user interactions (i.e., effort) or returning relevant results, as well as seller centric objectives, such as, maximizing profit. IQR offers principled exact and approximate solutions for generating relaxations that are demonstrated using multiple, large real datasets. © 2014 ACM.