A globally convergent incremental Newton method
Motivated by machine learning problems over large data sets and distributed optimization over networks, we develop and analyze a new method called incremental Newton method for minimizing the sum of a large number of strongly convex functions. We show that our method is globally convergent for a variable stepsize rule. We further show that under a gradient growth condition, convergence rate is linear for both variable and constant stepsize rules. By means of an example, we show that without the gradient growth condition, incremental Newton method cannot achieve linear convergence. Our analysis can be extended to study other incremental methods: in particular, we obtain a linear convergence rate result for the incremental GaussNewton algorithm under a variable stepsize rule.
newton method incremental methods convex optimization gaussnewton method strong convexity ekf algorithm 49m15: newton-type methods 90c30: nonlinear programming 90c06: large-scale problems 90c25: convex programming