  In this paper, we propose new proximal Newton-type methods for convex
optimization problems in composite form. The applications include model
predictive control (MPC) and embedded MPC. Our new methods are computationally
attractive since they do not require evaluating the Hessian at each iteration
while keeping fast convergence rate. More specifically, we prove the global
convergence is guaranteed and the superlinear convergence is achieved in the
vicinity of an optimal solution. We also develop several practical variants by
incorporating quasi-Newton and inexact subproblem solving schemes and provide
theoretical guarantee for them under certain conditions. Experimental results
on real-world datasets demonstrate the effectiveness and efficiency of new
methods.
