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Modified GaussNewton
"... scheme with worstcase guarantees for its global performance Yu. Nesterov∗ ..."
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scheme with worstcase guarantees for its global performance Yu. Nesterov∗
On the Gauss—Newton method for solving equations
, 2011
"... We use a combination of the center—Lipschitz condition with the Lipschitz condition condition on the Fréchet—derivative of the operator involved to provide a semilocal convergence analysis of the GaussNewton method to a solution of an equation. Using more precise estimates on the distances invol ..."
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We use a combination of the center—Lipschitz condition with the Lipschitz condition condition on the Fréchet—derivative of the operator involved to provide a semilocal convergence analysis of the GaussNewton method to a solution of an equation. Using more precise estimates on the distances
A GaussNewton Method for Convex Composite Optimization
, 1993
"... An extension of the GaussNewton method for nonlinear equations to convex composite optimization is described and analyzed. Local quadratic convergence is established for the minimization of h ffi F under two conditions, namely h has a set of weak sharp minima, C, and there is a regular point of th ..."
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Cited by 13 (1 self)
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An extension of the GaussNewton method for nonlinear equations to convex composite optimization is described and analyzed. Local quadratic convergence is established for the minimization of h ffi F under two conditions, namely h has a set of weak sharp minima, C, and there is a regular point
Convergence rates of the continuous regularized GaussNewton method
, 2002
"... In this paper a convergence proof is given for the continuous analog of the Gauss—Newton method for nonlinear illposed operator equations and convergence rates are obtained. Convergence for exact data is proved for nonmonotone operators under weaker source conditions than before. Moreover, nonline ..."
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Cited by 8 (5 self)
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In this paper a convergence proof is given for the continuous analog of the Gauss—Newton method for nonlinear illposed operator equations and convergence rates are obtained. Convergence for exact data is proved for nonmonotone operators under weaker source conditions than before. Moreover
Convergence analysis of a proximal GaussNewton method
, 2011
"... Abstract An extension of the GaussNewton algorithm is proposed to find local minimizers of penalized nonlinear least squares problems, under generalized Lipschitz assumptions. Convergence results of local type are obtained, as well as an estimate of the radius of the convergence ball. Some applicat ..."
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Cited by 2 (0 self)
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Abstract An extension of the GaussNewton algorithm is proposed to find local minimizers of penalized nonlinear least squares problems, under generalized Lipschitz assumptions. Convergence results of local type are obtained, as well as an estimate of the radius of the convergence ball. Some
Convergence and uniqueness properties of GaussNewton’s method
 Comput. Math. Appl
"... Abst ractThe generalized radius and center Lipschitz conditions with L average are introduced to investigate the convergence of GaussNewton's method for finding the nonlinear least squares solution of nonlinear equations. The radii of the convergence ball of GaussNewton's method and th ..."
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Cited by 11 (3 self)
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Abst ractThe generalized radius and center Lipschitz conditions with L average are introduced to investigate the convergence of GaussNewton's method for finding the nonlinear least squares solution of nonlinear equations. The radii of the convergence ball of GaussNewton's method
COUPLING TOPOLOGICAL GRADIENT AND GAUSSNEWTON METHOD
"... Topological asymptotic analysis is an emerging method that has been applied with success to shape optimization and shape inverse problems. However, it is not suitable for solving severely illposed inverse problems. It is a short term approach and it fails when applied to small inclusions detection ..."
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Cited by 1 (0 self)
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in elastographic imaging. We show in this paper that it is possible to solve this problem by coupling GaussNewton and topological gradient methods in a natural way. The data is the displacement under a small compression, only one component of the displacement is given. The inversion problem is solved in two steps
Multilevel GaussNewton methods for phase retrieval problems
 J. Phys. A
"... Abstract. The phase retrieval problem is of wide interest because it appears in a number of interesting application areas in physics. Several kinds of phase retrieval problems appeared in laser optics over the past decade. In this paper we consider the numerical solution of two phase retrieval probl ..."
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Cited by 1 (0 self)
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problems for an unknown smooth function f with compact support. We approximate f by a linear spline. The corresponding spline coefficients are iteratively determined by local Gauss–Newton methods, where convenient initial guesses are constructed by a multilevel strategy. We close with some numerical tests
Gauss–Newton reconstruction method for optical tomography using . . .
 JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER
, 2008
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