Abstract: A dynamic pricing algorithm is used to price a large set of items so that their aggregate margin is above a pre-specified level even under uncertain demand. The algorithm automatically hedges the profit loss associated to low-margin items with profit gains associated to higher-margin items, and does so even when the realized demand is different than the expected one. The algorithm leverages the separability of a re-formulation of the robust counterpart of the nominal revenue maximization problem. This separability results into a nested bisection algorithm where each iteration in the procedure requires only computation of a number of independent, one-dimensional optimization problems, one for each product to price. The algorithm is easily implemented in a parallel architecture such a multi-core computer or a cluster of computers, where each core handles an independent one-dimensional problem corresponding to an item and its data is stored locally.

Abstract: A dynamic pricing algorithm is used to price a large set of items so that their aggregate margin is above a pre-specified level even under uncertain demand. The algorithm automatically hedges the profit loss associated to low-margin items with profit gains associated to higher-margin items, and does so even when the realized demand is different than the expected one. The algorithm leverages the separability of a re-formulation of the robust counterpart of the nominal revenue maximization problem. This separability results into a nested bisection algorithm where each iteration in the procedure requires only computation of a number of independent, one-dimensional optimization problems, one for each product to price.

Abstract: Apparatus and method for classifying multi-dimensional biological data are described. In some embodiments, a methodology for deriving a linear classification rule can be used for predicting a biological activity or a biological state. Advantageously, the methodology described herein facilitates obtaining robust and sparse classifiers that account for uncertainty involved in real-world experiments and improve computational efficiency and ease of interpretation of results.