Local attractors of newton-type methods for constrained equations and complementarity problems with nonisolated solutions

Andreas Fischer(andreas.fischertu-dresden.de)
Alexey Izmailov(izmafccas.ru)
Mikhail Solodov(solodovimpa.br)

Abstract: For constrained equations with nonisolated solutions, we show that if the equation mapping is 2-regular 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 Newton-type methods is well-dened and necessarily converges to this specic 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 LP-Newton methods. Applications to smooth and piecewise smooth reformulations of complementarity problems are also discussed.

Keywords: constrained equation; complementarity problem; nonisolated solution; 2-regularity; Newton-type method; Levenberg{Marquardt method; LP-Newton method; piecewise Newton method

Category 1: Nonlinear Optimization (Nonlinear Systems and Least-Squares )

Category 2: Complementarity and Variational Inequalities

Citation: September 4, 2017

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Entry Submitted: 02/17/2018
Entry Accepted: 02/17/2018
Entry Last Modified: 02/17/2018

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