EFFICIENT SECOND-ORDER ALGORITHMS FOR STRUCTURED CONVEX COMPOSITE PROGRAMMING

Abstract

This work focuses on the development of convex optimization models and algorithms for solving large-scale problems arising in machine learning and data science. In particular, we focus on uncovering the hidden structure embedded in data, including the sparsity and clustering structure of the variables, and learning the global convex functional approximation of a given set of data points. For the potentially large-scale structured convex composite programming problems involved in the models, we design efficient second-order algorithms which fully exploit the structure of the data and the underlying Hessians to highly reduce the computational cost. Comprehensive numerical experiments demonstrate the superior performance of our proposed models and the efficiency and robustness of our proposed algorithms.