Review for NeurIPS paper: Convex optimization based on global lower second-order models

Summary and Contributions: This paper presents new second-order algorithms for the prototypical composite convex optimization problem. First, the paper introduces a new global second-order lower approximation. Based on this lower approximation model, the paper introduces a new second-order optimization algorithm. The proposed method successively minimizes the lower approximation model of the smooth term augmented by the nonsmooth term and constructs the solution to the original problem as a convex combination of the solutions to these subproblems. In this regard, it can be seen as a second-order modification of the Frank-Wolfe method, which considers a second-order lower model instead of the first-order.