In numerical analysis, Newton's method (also known as the Newton–Raphson method), named after Isaac Newton and Joseph Raphson, is a method for… (More)

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Highly Cited

2006

Highly Cited

2006

- Yurii Nesterov, Boris T. Polyak
- Math. Program.
- 2006

In this paper, we provide theoretical analysis for a cubic regularization of Newton method as applied to unconstrained… (More)

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Highly Cited

2004

Highly Cited

2004

- Glenn Fung, Olvi L. Mangasarian
- Comp. Opt. and Appl.
- 2004

A fast Newton method, that suppresses input space features, is proposed for a linear programming formulation of support vector… (More)

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Highly Cited

1999

Highly Cited

1999

- Chih-Jen Lin, Jorge J. Moré
- SIAM Journal on Optimization
- 1999

We analyze a trust region version of Newton’s method for bound-constrained problems. Our approach relies on the geometry of the… (More)

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Highly Cited

1996

Highly Cited

1996

- Stanley C. Eisenstat, Homer F. Walker
- SIAM J. Scientific Computing
- 1996

An inexact Newton method is a generalization ofNewton's method for solving F(x) 0, F n _ _ in, in which, at the kth iteration… (More)

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Highly Cited

1996

Highly Cited

1996

- Thomas F. Coleman, Yuying Li
- SIAM Journal on Optimization
- 1996

We propose a new algorithm, a reflective Newton method, for the minimization of a quadratic function of many variables subject to… (More)

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Highly Cited

1995

Highly Cited

1995

- Tjalling J. Ypma
- SIAM Review
- 1995

This expository paper traces the development of the Newton-Raphson method for solving nonlinear algebraic equations through the… (More)

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Highly Cited

1994

Highly Cited

1994

- Stanley C. Eisenstat, Homer F. Walker
- SIAM Journal on Optimization
- 1994

Inexact Newton methods for finding a zero of F 1 1 are variations of Newton's method in which each step only approximately… (More)

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Highly Cited

1993

Highly Cited

1993

Newton's method for solving a nonlinear equation of several variables is extended to a nonsmooth case by using the generalized… (More)

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Highly Cited

1989

Highly Cited

1989

- Dong C. Liu, Jorge Nocedal
- Math. Program.
- 1989

We study the numerical performance of a limited memory quasi Newton method for large scale optimization which we call the L BFGS… (More)

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Highly Cited

1988

Highly Cited

1988

- James Renegar
- Math. Program.
- 1988

The main motivation for this work was the idea that there should exist an easily understood polynomial time algorithm for linear… (More)

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