Accelerating Adaptive Cubic Regularization of Newton's Method via Random Sampling

Understand

In this paper, we consider an unconstrained optimization model where the objective is a sum of a large number of possibly nonconvex functions, though overall the objective is assumed to be smooth and convex.

• Our bid to solving such model uses the framework of cubic regularization of Newton's method.
• As well known, the crux in cubic regularization is its utilization of the Hessian information, which may be computationally expensive for large-scale problems.
• To tackle this, we resort to approximating the Hessian matrix via sub-sampling.