S. Jerad

TL;DR: Limited numerical experiments show that the new methods’ performance may be comparable to that of standard steepest descent, despite using significantly less information, and that this performance is relatively insensitive to noise.

TL;DR: It is shown that excellent complexity bounds for adaptive regularization methods are also valid for the new algorithm, despite the fact that significantly less information is used.

TL;DR: In this article , a parametric class of trust-region algorithms for unconstrained nonconvex optimization is considered, where the value of the objective function is never computed, and the rate of convergence of methods in the class is analyzed and is shown to be identical to that known for first-order optimization methods using both function and gradients values.

TL;DR: An adaptive regularization algorithm for unconstrained nonconvex optimization uses derivatives only, achieving optimal complexity bounds despite reduced information, finding approximate minimizers in at most iterations with varying degrees of derivatives used.