To address these issues, we present TORO. In its first phase, TORO also involves a sampling strategy to obtain candidates for the vectors a * , b * and c * , but we use a simplification of the objective function, allowing us to avoid employing GD. This simpler objective has closed-form updates that accelerate computation and eliminate GD-related problems such as being stuck in local minima, zigzagging, choosing the learning rate and gradient explosion or vanishing, among others. In fact, with no outliers, our approach only requires a single update step to reach the solution. However, handling outliers is fundamental to solving the indexing problem. Consequently, we introduce a robust optimization technique akin to the Least Trimmed Squares (LTS) method . This technique introduces a slight constant overhead on the number of updates compared to the regular Least Squares (LS) method. However, it enables us to robustly handle any number of outliers without incurring the iterative demands often associated with GD methods.