Solving the Trust-Region Subproblem using the Lanczos Method

By N. Gould, Stefano Lucidi, Massimo Roma, Philippe L. Toint. 1999

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

Full Waveform Inversion and the Truncated Newton Method (2013, methodology): “[26], who propose a sophistication of the initial Steihaug–Toint algorithm using the Lanczos algorithm to mitigate this difficulty.”
Optimization Methods for Supervised Machine Learning: From Linear Models to Deep Learning (2017, methodology): “Two well-known algorithms that serve this purpose are the Steihaug-Toint CG method [79, 82] and GLTR [32].”
Training Deep and Recurrent Networks with Hessian-Free Optimization (2012, methodology): “This is known as the Steihaug-Toint method, and it can be shown [12] that, provided CG is initialized from a zero starting solution and no preconditioning is used, the norm of the solution will increase monotonically and that if CG is truncated in the manner described above, the resultant solution δ”
trlib: a vector-free implementation of the GLTR method for iterative solution of the trust region problem (2016, methodology): “Contributions We introduce trlib which is a new vector-free implementation of the GLTR (Generalized Lanczos Trust Region) method for solving the trust region subproblem.”
Finding Optimal Algorithmic Parameters Using Derivative-Free Optimization (2006, methodology): “problems are solved by means of the Generalized Lanczos method for Trust Regions GLTR [16, 18].”
Adaptive cubic regularisation methods for unconstrained optimization. Part I: motivation, convergence and numerical results (2011, methodology): “2 and the specially-designed algorithm given in [14]), which is potentially expensive in the case of B, but far less so for Tj , especially since we have that of Tj−1 as a starting estimate—in which case Theorem 6.”
CUTEr and SifDec: A constrained and unconstrained testing environment, revisited (2003, methodology): “Since 1993, the CUTE environment and test problems have been widely used by the community of optimization software developers [1,3,4,6,7,10,11,12,13, 14,21,23,25, 26 ,27,31,32,36,37,38,39,40,41,42].”
Numerical optimization (2004, methodology): “GLTR [145] offers a Newton–Lanczos method.”