Big-data applications have initiated a resurgence of optimization methods with inexpensive iterations, namely first-order methods. The efficiency of first-order methods has been shown for several well conditioned problems in big-data optimization. However, their practical convergence might be slow on ill-conditioned/pathological instances.
In this talk we will discuss Newton-type methods, which aim to exploit the trade-off between inexpensive iterations and robustness. Two methods will be presented, a robust block coordinate descent method and a primal-dual Newton conjugate gradients method. We will discuss theoretical properties of the methods and we will present numerical experiments on big-data applications such as regression, machine learning and image processing.
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