Trust region methods are a class of numerical methods for optimization. Unlike line search
type methods where a line search is carried out in each iteration, trust region methods …

Optimization on Riemannian manifolds-the result of smooth geometry and optimization
merging into one elegant modern framework-spans many areas of science and engineering …

Yurii Nesterov Second Edition Page 1 Springer Optimization and Its Applications 137 Yurii
Nesterov Lectures on Convex Optimization Second Edition Page 2 Springer Optimization and …

This book is on conjugate gradient methods for unconstrained optimization. The concept of
conjugacy was introduced by Magnus Hestenes and Garrett Birkhoff in 1936 in the context of …

We consider variants of trust-region and adaptive cubic regularization methods for non-
convex optimization, in which the Hessian matrix is approximated. Under certain condition …

Optimization algorithms can see their local convergence rates deteriorate when the Hessian
at the optimum is singular. These singularities are inescapable when the optima are non …

Abstract An Adaptive Regularisation algorithm using Cubics (ARC) is proposed for
unconstrained optimization, generalizing at the same time an unpublished method due to …

While first-order optimization methods, such as SGD are popular in machine learning (ML),
they come with well-known deficiencies, including relatively-slow convergence, sensitivity to …

Abstract An Adaptive Regularisation framework using Cubics (ARC) was proposed for
unconstrained optimization and analysed in Cartis, Gould and Toint (Part I, Math Program …

We consider the minimization of a nonconvex quadratic form regularized by a cubic term,
which may exhibit saddle points and a suboptimal local minimum. Nonetheless, we prove …