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298
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 ..."
Abstract

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
Radiality and semismoothness
 Control and Cybernetics
"... Abstract: We provide sufficient conditions for radiality and semismoothness. In general Banach spaces, we show that calmness ensures Diniradiality as well as Diniconvexity of solution set to inequality systems. In finite dimensional spaces, we introduce the concept of Clarkeradiality and semismoo ..."
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Cited by 2 (0 self)
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Abstract: We provide sufficient conditions for radiality and semismoothness. In general Banach spaces, we show that calmness ensures Diniradiality as well as Diniconvexity of solution set to inequality systems. In finite dimensional spaces, we introduce the concept of Clarke
Semismooth Support Vector Machines
, 2000
"... The linear support vector machine can be posed as a quadratic program in a variety of ways. In this paper, we look at a formulation using the twonorm for the misclassification error that leads to a positive definite quadratic program with a single equality constraint when the Wolfe dual is taken. T ..."
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Cited by 2 (0 self)
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. The quadratic term is a small rank update to a positive definite matrix. We reformulate the optimality conditions as a semismooth system of equations using the FischerBurmeister function and apply a damped Newton method to solve the resulting problem. The algorithm is shown to converge from any starting point
A Semismooth Equation Approach To The Solution Of Nonlinear Complementarity Problems
, 1995
"... In this paper we present a new algorithm for the solution of nonlinear complementarity problems. The algorithm is based on a semismooth equation reformulation of the complementarity problem. We exploit the recent extension of Newton's method to semismooth systems of equations and the fact that ..."
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Cited by 106 (12 self)
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In this paper we present a new algorithm for the solution of nonlinear complementarity problems. The algorithm is based on a semismooth equation reformulation of the complementarity problem. We exploit the recent extension of Newton's method to semismooth systems of equations and the fact
SEMISMOOTH METHODS FOR LINEAR AND NONLINEAR
, 2006
"... The optimality conditions of a nonlinear secondorder cone program can be reformulated as a nonsmooth system of equations using a projection mapping. This allows the application of nonsmooth Newton methods for the solution of the nonlinear secondorder cone program. Conditions for the local quadra ..."
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The optimality conditions of a nonlinear secondorder cone program can be reformulated as a nonsmooth system of equations using a projection mapping. This allows the application of nonsmooth Newton methods for the solution of the nonlinear secondorder cone program. Conditions for the local
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
THE JOSEPHY–NEWTON METHOD FOR SEMISMOOTH GENERALIZED EQUATIONS AND SEMISMOOTH SQP FOR OPTIMIZATION
, 2011
"... While generalized equations with differentiable singlevalued base mappings and the associated Josephy–Newton method have been studied extensively, the setting with semismooth base mapping had not been previously considered (apart from the two special cases of usual nonlinear equations and of Karush ..."
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Cited by 4 (4 self)
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and of KarushKuhnTucker optimality systems). We introduce for the general semismooth case appropriate notions of solution regularity and prove local convergence of the corresponding Josephy–Newton method. As an application, we immediately recover the known primaldual local convergence properties
The Semismooth Algorithm for Large Scale Complementarity Problems
, 1999
"... Complementarity solvers are continually being challenged by modelers demanding improved reliability and scalability. Building upon a strong theoretical background, the semismooth algorithm has the potential to meet both of these requirements. We briefly discuss relevant theory associated with th ..."
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Cited by 21 (7 self)
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Complementarity solvers are continually being challenged by modelers demanding improved reliability and scalability. Building upon a strong theoretical background, the semismooth algorithm has the potential to meet both of these requirements. We briefly discuss relevant theory associated
Results 1  10
of
298