Newton’s method with feasible inexact projections for solving constrained generalized equations

Fabiana R. Oliveira (), Orizon P. Ferreira () and Gilson N. Silva ()
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Fabiana R. Oliveira: Universidade Federal de Goiás
Orizon P. Ferreira: Universidade Federal de Goiás
Gilson N. Silva: Universidade Federal do Oeste da Bahia

Computational Optimization and Applications, 2019, vol. 72, issue 1, No 5, 159-177

Abstract: Abstract This paper aims to address a new version of Newton’s method for solving constrained generalized equations. This method can be seen as a combination of the classical Newton’s method applied to generalized equations with a procedure to obtain a feasible inexact projection. Using the contraction mapping principle, we establish a local analysis of the proposed method under appropriate assumptions, namely metric regularity or strong metric regularity and Lipschitz continuity. Metric regularity is assumed to guarantee that the method generates a sequence that converges to a solution. Under strong metric regularity, we show the uniqueness of the solution in a suitable neighborhood, and that all sequences starting in this neighborhood converge to this solution. We also require the assumption of Lipschitz continuity to establish a linear or superlinear convergence rate for the method.

Keywords: Constrained generalized equations; Newton’s method; Feasible inexact projection; Lipschitz continuity; Metric regularity; Strong metric regularity; Local convergence; 65K15; 49M15; 90C30 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s10589-018-0040-0

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