Topic: Optimization with Uncertain, Online and Massive Data
We present several analytic models and computational algorithms dealing with online/dynamic, structured and/or massively distributed data. Specifically, we discuss ：
• Distributionally Robust Optimization Models, where many problems can be efficiently solved when the associated uncertain data possess no priori distributions;
• Near-Optimal Online Linear Programming Algorithms, where the matrix data is revealed column by column along with the objective function and a decision has to be made as soon as a variable arrives;
•Sparse regression with Non-convex Regularization, where we give sparse and structure characterizations for every KKT stationary solution of the problem;
• Alternating Direction Method of Multipliers (ADMM) for large-scale data, where we give an example to show that the direct extension of ADMM for three-block convex minimization problems is not necessarily convergent, and propose simple and effective convergent variants.