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Error Bounds and Superlinear Convergence Analysis of Some NewtonType Methods in Optimization
, 1998
"... We show that, for some Newtontype methods such as primaldual interiorpoint path following methods and ChenMangasarian smoothing methods, local superlinear convergence can be shown without assuming the solutions are isolated. The analysis is based on local error bounds on the distance from the ite ..."
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We show that, for some Newtontype methods such as primaldual interiorpoint path following methods and ChenMangasarian smoothing methods, local superlinear convergence can be shown without assuming the solutions are isolated. The analysis is based on local error bounds on the distance from
CONVERGENCE CONDITIONS FOR NEWTONTYPE METHODS APPLIED TO COMPLEMENTARITY SYSTEMS WITH NONISOLATED SOLUTIONS∗
, 2015
"... Abstract. We consider a class of Newtontype methods for constrained systems of equations that involve complementarity conditions. In particular, at issue are the constrained Levenberg–Marquardt method and the recently introduced LinearProgrammingNewton method, designed for the difficult case when ..."
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Abstract. We consider a class of Newtontype methods for constrained systems of equations that involve complementarity conditions. In particular, at issue are the constrained Levenberg–Marquardt method and the recently introduced LinearProgrammingNewton method, designed for the difficult case
Convergence rates of recursive Newtontype methods for multifrequency scattering problems
"... We are concerned with the reconstruction of a soundsoft obstacle using far field measurements of the scattered waves associated with incident plane waves sent from one direction but at multiple frequencies. We define, for each frequency, the observable shape as the one which is described by finitel ..."
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by finitely many modes and produces a far field pattern close to the measured one. In the first step, we propose a recursive Newtontype method for the reconstruction of the observable shape at the highest frequency knowing an estimate of the observable shape at the lowest frequency. We analyze its
A Validated Newton Type Method for Nonlinear Equations
 Interval Computations
, 1994
"... Considered is an iterative procedure of Newton type for a nonlinear equation f(x) = 0 in a given interval X0. Global quadratic convergence of the method is proved assuming that f ′ is Lipschitzian. An algorithm with result verification is constructed using computer interval arithmetic and some nume ..."
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Cited by 3 (1 self)
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Considered is an iterative procedure of Newton type for a nonlinear equation f(x) = 0 in a given interval X0. Global quadratic convergence of the method is proved assuming that f ′ is Lipschitzian. An algorithm with result verification is constructed using computer interval arithmetic and some
Institut für Numerische und Angewandte Mathematik Iteratively regularized Newtontype methods with general data misfit functionals and applications to Poisson data
, 2012
"... Iteratively regularized Newtontype methods for general data misfit functionals and applications to Poisson data ..."
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Iteratively regularized Newtontype methods for general data misfit functionals and applications to Poisson data
Fast newtontype methods for the least squares nonnegative matrix approximation problem
 Statistical Analysis and Data Mining
, 2008
"... Nonnegative Matrix Approximation is an effective matrix decomposition technique that has proven to be useful for a wide variety of applications ranging from document analysis and image processing to bioinformatics. There exist a few algorithms for nonnegative matrix approximation (NNMA), for example ..."
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Cited by 48 (6 self)
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for the leastsquares NNMA problem, which are not only theoretically wellfounded, but also overcome many of the deficiencies of other methods. In particular, we use nondiagonal gradient scaling to obtain rapid convergence. Our methods provide numerical results superior to both Lee & Seung’s method as well
M.J.:A unified convergence theory for Newtontype methods for zeros of nonlinear operators in Banach spaces
 BIT
, 2002
"... The paper is concerned with the convergence problem of Newton type methods for finding zeros of nonlinear operators in Banach spaces. Some families of nonlinear operators are defined by different Lipschitz conditions and an “universal constant ” is introduced so that a unified convergence determina ..."
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Cited by 2 (1 self)
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The paper is concerned with the convergence problem of Newton type methods for finding zeros of nonlinear operators in Banach spaces. Some families of nonlinear operators are defined by different Lipschitz conditions and an “universal constant ” is introduced so that a unified convergence
Article NewtonType Methods on Generalized Banach Spaces and Applications in Fractional Calculus
"... algorithms ..."
Optimal Newtontype methods for nonconvex smooth optimization problems
, 2011
"... We consider a general class of secondorder iterations for unconstrained optimization that includes regularization and trustregion variants of Newton’s method. For each method in this class, we exhibit a smooth, boundedbelow objective function, whose gradient is globally Lipschitz continuous withi ..."
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Cited by 2 (1 self)
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We consider a general class of secondorder iterations for unconstrained optimization that includes regularization and trustregion variants of Newton’s method. For each method in this class, we exhibit a smooth, boundedbelow objective function, whose gradient is globally Lipschitz continuous
NEWTONTYPE METHODS FOR OPTIMIZATION PROBLEMS WITHOUT CONSTRAINT QUALIFICATIONS
 SIAM J. OPTIMIZATION
, 2004
"... We consider equalityconstrained optimization problems, where a given solution may not satisfy any constraint qualification, but satisfies the standard secondorder sufficient condition for optimality. Based on local identification of the rank of the constraints degeneracy via the singularvalue d ..."
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Cited by 17 (13 self)
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value decomposition, we derive a modified primaldual optimality system whose solution is locally unique, nondegenerate, and thus can be found by standard Newtontype techniques. Using identification of active constraints, we further extend our approach to mixed equality and inequalityconstrained problems
Results 21  30
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168,343