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Andreas Fischer(andreas.fischertudresden.de) Abstract: For constrained equations with nonisolated solutions, we show that if the equation mapping is 2regular at a given solution with respect to a direction in the null space of the Jacobian, and this direction is interior feasible, then there is an associated domain of starting points from which a family of Newtontype methods is welldened and necessarily converges to this specic solution (despite degeneracy, and despite that there are other solutions nearby). We note that unlike the common settings of convergence analyses, our assumptions subsume that a local Lipschitzian error bound does not hold for the solution in question. Our results apply to constrained and projected variants of the Gauss{Newton, Levenberg{Marquardt, and LPNewton methods. Applications to smooth and piecewise smooth reformulations of complementarity problems are also discussed. Keywords: constrained equation; complementarity problem; nonisolated solution; 2regularity; Newtontype method; Levenberg{Marquardt method; LPNewton method; piecewise Newton method Category 1: Nonlinear Optimization (Nonlinear Systems and LeastSquares ) Category 2: Complementarity and Variational Inequalities Citation: September 4, 2017 Download: [PDF] Entry Submitted: 02/17/2018 Modify/Update this entry  
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