## Optimal Newton-type methods for nonconvex smooth optimization problems

We consider a general class of second-order iterations for unconstrained optimization that includes regularization and trust-region variants of Newton’s method. For each method in this class, we exhibit a smooth, bounded-below objective function, whose gradient is globally Lipschitz continuous within an open convex set containing any iterates encountered and whose Hessian is $\alpha-$Holder continuous (for … Read more

## AN OPTIMAL ALGORITHM FOR CONSTRAINED DIFFERENTIABLE CONVEX OPTIMIZATION

We describe three algorithms for solving differentiable convex optimization problems constrained to simple sets in $\R^n$, i.e., sets on which it is easy to project an arbitrary point. The first two algorithms are optimal in the sense that they achieve an absolute precision of $\varepsilon$ in relation to the optimal value … Read more