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A nonmonotone semismooth inexact Newton method
"... In this work we propose a variant of the inexact Newton method for the solution of semismooth nonlinear systems of equations. We introduce a nonmonotone scheme, which couples the inexact features with the nonmonotone strategies. For the nonmonotone scheme, we present the convergence theorems. Finall ..."
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In this work we propose a variant of the inexact Newton method for the solution of semismooth nonlinear systems of equations. We introduce a nonmonotone scheme, which couples the inexact features with the nonmonotone strategies. For the nonmonotone scheme, we present the convergence theorems
A Nonmonotone Inexact Newton Method
 Optim. Methods Softw
, 2005
"... In this paper we describe a variant of the Inexact Newton method for solving nonlinear systems of equations. We define a nonmonotone Inexact Newton step and a nonmonotone backtracking strategy. For this nonmonotone Inexact Newton scheme we present the convergence theorems. Finally, we show how we ca ..."
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Cited by 3 (2 self)
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In this paper we describe a variant of the Inexact Newton method for solving nonlinear systems of equations. We define a nonmonotone Inexact Newton step and a nonmonotone backtracking strategy. For this nonmonotone Inexact Newton scheme we present the convergence theorems. Finally, we show how we
A Semismooth Inexact Newtontype Method for the Solution of Optimal Power Flow Problem
"... Abstract: The paper presents a semismooth inexact Newtontype method for solving optimal power flow (OPF) problem. By introducing the nonlinear complementarity problem (NCP) function, the KarushKuhnTucker (KKT) conditions of OPF model are transformed equivalently into a set of semismooth nonlinea ..."
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Abstract: The paper presents a semismooth inexact Newtontype method for solving optimal power flow (OPF) problem. By introducing the nonlinear complementarity problem (NCP) function, the KarushKuhnTucker (KKT) conditions of OPF model are transformed equivalently into a set of semismooth
Inexact Newton Methods For Semismooth Equations With Applications To Variational Inequality Problems
"... : We consider the local behaviour of inexact Newton methods for the solution of a semismooth system of equations. In particular, we give a complete characterization of the Qsuperlinear and Qquadratic convergence of inexact Newton methods. We then apply these results to a particular semismooth syst ..."
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Cited by 19 (6 self)
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: We consider the local behaviour of inexact Newton methods for the solution of a semismooth system of equations. In particular, we give a complete characterization of the Qsuperlinear and Qquadratic convergence of inexact Newton methods. We then apply these results to a particular semismooth
InexactNewton methods for semismooth systems of equations with blockangular structure
, 1998
"... Systems of equations with blockangular structure have applications in evolution problems coming from Physics, Engineering and Economy. Many times, these systems are timestage formulations of mathematical models that consist of mathematical programming problems, complementarity, or other equilibriu ..."
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Cited by 1 (0 self)
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. In this paper we define two inexactNewton algorithms for semismooth blockangular systems and we prove local and superlinear convergence. Keywords. Semismooth equations, Nonlinear systems, InexactNewton methods, decomposition. Institute of Mathematics, University of Novi Sad, Trg Dositeja Obradovi
Choosing the Forcing Terms in an Inexact Newton Method
 SIAM J. SCI. COMPUT
, 1994
"... An inexact Newton method is a generalization of Newton's method for solving F(x) = 0, F:/ /, in which, at the kth iteration, the step sk from the current approximate solution xk is required to satisfy a condition ]lF(x) + F'(x)s]l _< /]lF(xk)]l for a "forcing term" / [0,1). I ..."
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Cited by 161 (6 self)
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An inexact Newton method is a generalization of Newton's method for solving F(x) = 0, F:/ /, in which, at the kth iteration, the step sk from the current approximate solution xk is required to satisfy a condition ]lF(x) + F'(x)s]l _< /]lF(xk)]l for a "forcing term" / [0
Inexact Newton Methods for Solving Nonsmooth Equations
 Journal of Computational and Applied Mathematics
, 1999
"... This paper investigates inexact Newton methods for solving systems of nonsmooth equations. We define two inexact Newton methods for locally Lipschitz functions and we prove local (linear and superlinear) convergence results under the assumptions of semismoothness and BDregularity at the solution. W ..."
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Cited by 30 (9 self)
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This paper investigates inexact Newton methods for solving systems of nonsmooth equations. We define two inexact Newton methods for locally Lipschitz functions and we prove local (linear and superlinear) convergence results under the assumptions of semismoothness and BDregularity at the solution
Semismooth Equations ∗
"... [Article] Hybrid Newtontype method for a class of semismooth equations ..."
JACOBIAN SMOOTHING INEXACT NEWTON METHOD FOR NCP WITH A SPECIAL CHOICE OF FORCING PARAMETERS
"... Abstract. The inexact Newton method with a special choice of forcing parameters is proposed for solving nonlinear complementarity problems. This method belongs to the class of Jacobian smoothing methods. Linear system is solved approximately in every iteration. The sequence of forcing terms controls ..."
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controls the accuracy level of the approximate solution and influences the behavior of the method. Globalization strategy is based on nonmonotone rule. AMS Mathematics Subject Classification (2000): 65H10; 90C33 Key words and phrases: Nonlinear complementarity problems, inexact Newton method, semismooth
Semismooth Newton methods for operator equations in function spaces
, 2000
"... We develop a semismoothness concept for nonsmooth superposition operators in function spaces. The considered class of operators includes NCPfunctionbased reformulations of infinitedimensional nonlinear complementarity problems, and thus covers a very comprehensive class of applications. Our resul ..."
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Cited by 50 (3 self)
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these semismoothness results to develop a Newtonlike method for nonsmooth operator equations and prove its local qsuperlinear convergence to regular solutions. If the underlying operator is fforder semismoothness, convergence of qorder 1 + ff is proved. We also establish the semismoothness of composite operators
Results 1  10
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