adaptive regularized framework using cubics

A Line-Search Algorithm Inspired by the Adaptive Cubic Regularization Framework and Complexity Analysis

Published: 2017/06/16, Updated: 2018/05/29

Adaptive regularized framework using cubics has emerged as an alternative to line-search and trust-region algorithms for smooth nonconvex optimization, with an optimal complexity amongst second-order methods. In this paper, we propose and analyze the use of an iteration dependent scaled norm in the adaptive regularized framework using cubics. Within such scaled norm, the obtained method … Read more

On the use of the energy norm in trust-region and adaptive cubic regularization subproblems

Published: 2017/04/26

Elhoucine Bergou

Youssef Diouane

Serge Gratton

Unconstrained Optimization adaptive regularized framework using cubics, conjugate gradient method, energy norm, krylov subspace methods, line search algorithm, nonlinear optimization, trust-region methods, unconstrained optimization

We consider solving unconstrained optimization problems by means of two popular globalization techniques: trust-region (TR) algorithms and adaptive regularized framework using cubics (ARC). Both techniques require the solution of a so-called “subproblem” in which a trial step is computed by solving an optimization problem involving an approximation of the objective function, called “the model”. The … Read more