Newton-Type Minimization via the Lanczos Method

By Stephen G. Nash. 1984

Subfields: Mathematical Optimization, Numerical Methods & Scientific Computing

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Citations in the corpus

Prediction uncertainty and optimal experimental design for learning dynamical systems. (2015, methodology): “The data ﬁtting problem is an unconstrained minimization problem, and was solved using the Scipy implementation of the Newton conjugate-gradient algorithm 26,27 .”
The State of the Art (2001, unknown): “work by Griewank and Toint [67], Nash [92], Buckley and Lenir [18], Byrd, Nocedal and Schnabel [24] and Liu and Nocedal [83].”
Numerical optimization (2004, methodology): “Freely available packages include TN/TNBC [220] and TNPACK [275].”
CONSTRAINING THE MILKY WAY POTENTIAL WITH A SIX-DIMENSIONAL PHASE-SPACE MAP OF THE GD-1 STELLAR STREAM (2009, methodology): “The maximization is performed using the Truncated Newton method(Nash 1984).”
Optimization and uncertainty analysis of ODE models using 2nd order adjoint sensitivity analysis (2018, methodology): “This information can be exploited by optimization methods such as truncated Newton (Nash, 1984) or accelerated conjugate gradient (Andrei, 2009) algorithms, which are suited for large-scale optimization problems.”
A continuation/GMRES method for fast computation of nonlinear receding horizon control (2004, methodology): “…algorithm C/GMRES is compared with a conventional algorithm (Ohtsuka, 1998) based on the backward sweep method, and two general-purpose optimization codes based on the limited-memory BFGS method (L-BFGS) (Liu & Nocedal, 1989; Nocedal, 1990) and on the truncated Newton method (Nash, 1984a, b).”
Solving the Trust-Region Subproblem using the Lanczos Method (1999, methodology): “The Lanczos basis has previously been used by [10]—to convexify the quadratic model—and [8]—to compute good directions of negative curvature—within linesearch-based methods for unconstrained minimization.”
On the Use of Stochastic Hessian Information in Optimization Methods for Machine Learning (2011, background): “For k ¼ 0; 1; : : : , until a convergence test is satisfied: 1.”
Training Deep and Recurrent Networks with Hessian-Free Optimization (2012, background): “Different algorithms that use many of the same key principles have appeared in the literatures of various communities under different names such as Newton-CG, CG-Steihaug, Newton-Lanczos, and Truncated Newton [27, 28], but applications to machine learning and especially neural networks, have been li”