1. A matrix completion problem used by an online retailer to identify new routes/travels that are more likely to be preferred by a client. This problem, based on real fintech data, considers millions of clients and more than 80 different products. This leads to a structured semidefinite programming problem with semidefinite matrices with millions of rows and columns.

2. A feature selection problem that arises from a gas station pricing problem from marketing. In this application the feature selection problem, which seeks to identify the gas stations used for comparison, considers more that 100.000 original parameters and has pricing data for more than two years every 5 minutes.

Professor Ordóñez has domain knowledge and access to real data for both of these industrial application problems.

The expected methodological contributions for the feature selection problem include : 1) developing a Benders decomposition version of the decomposition problem, 2) comparing it with the column generation version that has been developed and 3) evaluate the impact of these decomposition solution strategies of the continuous feature selection problem on the integer version of the problem.

We expect to publish the results from this collaboration in top international journals and will explore the benefit of these methods in real world applications in international companies where these problems come from.

During professor Ordóñez visit we plan to advance research in the following areas : 1) identifying the most promising solution methods for each application, 2) Identify the Benders decomposition strategy for the feature selection problem and 3) Integrate these decomposition strategies in a branch-and-price or branch- and-cut scheme to solve the integer version of the feature selection problem.

During his two week stay, in addition to advancing research, professor Ordóñez will give a research talk and will collaborate in advising my Ph.D. student Rui MA who is also working on the feature selection model for predicting frost-events.