ARCq: a new adaptive regularization by cubics

On the convergence and worst-case complexity of trust-region and regularization methods for unconstrained optimization

(2014) Geovani N. Grapiglia et al.   MATHEMATICAL PROGRAMMING

Nonlinear stepsize control, trust regions and regularizations for unconstrained optimization

(2011) Philippe L. Toint   OPTIMIZATION METHODS & SOFTWARE

Adaptive cubic regularisation methods for unconstrained optimization. Part II: worst-case function- and derivative-evaluation complexity

(2010) Coralia Cartis et al.   MATHEMATICAL PROGRAMMING

On the Complexity of Steepest Descent, Newton's and Regularized Newton's Methods for Nonconvex Unconstrained Optimization Problems

(2010) C. Cartis et al.   SIAM JOURNAL ON OPTIMIZATION

Adaptive cubic regularisation methods for unconstrained optimization. Part I: motivation, convergence and numerical results

(2009) Coralia Cartis et al.   MATHEMATICAL PROGRAMMING

Recursive Trust-Region Methods for Multiscale Nonlinear Optimization

(2008) Serge Gratton et al.   SIAM JOURNAL ON OPTIMIZATION