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M. Nashed, X. Chen (1993)
Convergence of Newton-like methods for singular operator equations using outer inversesNumerische Mathematik, 66
Convergence of Newton's method for singular smooth and nonsmooth equations using outer inverses
Xiaojun Chen, Z. Nashed, L. Qi (1997)
Convergence of Newton's Method for Singular Smooth and Nonsmooth Equations Using Adaptive Outer InversesSIAM J. Optim., 7
Tetsuro Yamamoto (1986)
A method for finding sharp error bounds for Newton's method under the Kantorovich assumptionsNumerische Mathematik, 49
G. Alefeld, A. Gienger, F. Potra (1994)
Efficient numerical validation of solutions of nonlinear systemsSIAM Journal on Numerical Analysis, 31
L. Qi, Xiaojun Chen (1995)
A Globally Convergent Successive Approximation Method for Severely Nonsmooth EquationsSiam Journal on Control and Optimization, 33
(1990)
Newton methods for B-diierentiable equations
M. Heinkenschloss, C. Kelley, H. Tran (1992)
Fast algorithms for nonsmooth compact fixed-point problemsSIAM Journal on Numerical Analysis, 29
Shih-Ping Han, J. Pang, N. Rangaraj (1992)
Globally Convergent Newton Methods for Nonsmooth EquationsMath. Oper. Res., 17
G. Alefeld, J. Herzberger, J. Rokne (1983)
Introduction to Interval Computation
Ramon Moore, L. Qi (1982)
A Successive Interval Test for Nonlinear SystemsSIAM Journal on Numerical Analysis, 19
(1992)
Fast algorithms for nons- mooth compact xed point problems
J. Ortega, W. Rheinboldt (2014)
Iterative solution of nonlinear equations in several variables
L. Qi, Jie Sun (1993)
A nonsmooth version of Newton's methodMathematical Programming, 58
L. Qi, X. Chen (1995)
A globally convergent successive approximation method for nonsmooth equationsSIAM J. Control Optim., 33
B. Kummer (1988)
NEWTON's METHOD FOR NON-DIFFERENTIABLE FUNCTIONSAdvances in Mathematical Optimization
(1988)
Newton's method for non-diierentiable functions
A. Frommer, G. Mayer (1990)
On the R -order of Newton-like methods for enclosing solutions of nonlinear equationsSIAM Journal on Numerical Analysis, 27
L. Qi (1993)
Convergence Analysis of Some Algorithms for Solving Nonsmooth EquationsMath. Oper. Res., 18
B. Kummer (1988)
Advances in Mathematical Optimization
(1983)
Introduction to interval computations
Xiaojun Chen (1996)
Convergence of the BFGS Method for LC 1 Convex Constrained OptimizationSiam Journal on Control and Optimization, 34
D. Ralph (1994)
Global Convergence of Damped Newton's Method for Nonsmooth Equations via the Path SearchMath. Oper. Res., 19
陳 小君 (1990)
On the convergence of Broyden-like methods for nonlinear equations with nondifferentiable terms
J. Pang, Liqun Qi (1993)
Nonsmooth Equations: Motivation and AlgorithmsSIAM J. Optim., 3
R. Mifflin (1977)
Semismooth and Semiconvex Functions in Constrained OptimizationSiam Journal on Control and Optimization, 15
(1990)
Newton methods for B-differentiable
C. Ip, J. Kyparisis (1992)
Local convergence of quasi-Newton methods for B-differentiable equationsMathematical Programming, 56
(1990)
Validated methods for solving nonlinear systems
Xiaojun Chen (1990)
On the convergence of Broyden-like methods for nonlinear equations with nondifferentiable termsAnnals of the Institute of Statistical Mathematics, 42
A. Frommer, G. Mayer (1989)
Safe bounds for the solutions of nonlinear problems using a parallel multisplitting methodComputing, 42
Chen Xiaojun, W. Deren (1989)
On the optimal properties of the krawczyk-type interval operator∗International Journal of Computer Mathematics, 29
Xiaojun Chen, Tetsuro Yamamoto (1992)
On the convergence of some quasi-Newton methods for nonlinear equations with nondifferentiable operatorsComputing, 49
J. Pang (1990)
Newton's Method for B-Differentiable EquationsMath. Oper. Res., 15
(1988)
Newton's method for non-di erentiable functions, in J. Gud- dat
(1990)
Newton methods for B-di erentiable equations
F. Clarke (1983)
Optimization And Nonsmooth Analysis
Ladislav Lukan (1994)
Inexact trust region method for large sparse systems of nonlinear equationsJournal of Optimization Theory and Applications, 81
L. Qi (1982)
A Note on the Moore Test for Nonlinear SystemsSIAM Journal on Numerical Analysis, 19
This paper proposes a verification method for the existence of solutions of nonsmooth equations. We generalize the Krawczyk operator to nonsmooth equations by using the mean-value theorem for nonsmooth functions. We establish a semi-local convergence theorem for the generalized Newton method for nonsmooth equations. The proposed method is a combination of the generalized Krawczyk operator and the semi-local convergence theorem.
Computing – Springer Journals
Published: Aug 4, 2007
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