In many optimization problems arising from scientific, engineering and artificial intelligence
applications, objective and constraint functions are available only as the output of a black …

There has been much recent interest in finding unconstrained local minima of smooth
functions, due in part to the prevalence of such problems in machine learning and robust …

Do you know the difference between an optimist and a pessimist? The former believes we
live in the best possible world, and the latter is afraid that the former might be right.… In that …

We establish or refute the optimality of inexact second-order methods for unconstrained
nonconvex optimization from the point of view of worst-case evaluation complexity …

An adaptive regularization algorithm is proposed that uses Taylor models of the objective of
order p, p≥ 2, of the unconstrained objective function, and that is guaranteed to find a first …

Concise complexity analyses are presented for simple trust region algorithms for solving
unconstrained optimization problems. In contrast to a traditional trust region algorithm, the …

This work presents a novel matrix-based method for constructing an approximation Hessian
using only function evaluations. The method requires less computational power than …

For the unconstrained optimization of black box functions, this paper introduces a new
randomized algorithm called VRBBO. In practice, VRBBO matches the quality of other state …

Necessary conditions for high-order optimality in smooth nonlinear constrained optimization
are explored and their inherent intricacy discussed. A two-phase minimization algorithm is …

An adaptive regularization algorithm (AR GN) for unconstrained nonlinear minimization is
considered, which uses a model consisting of a Taylor expansion of arbitrary degree and …