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


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Article Info

DATE

2018-10-26

AUTHORS

Fabiana R. de Oliveira, Orizon P. Ferreira, Gilson N. Silva

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. More... »

PAGES

159-177

References to SciGraph publications

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  • 2018-01-25. Quasi-Newton methods for constrained nonlinear systems: complexity analysis and applications in COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
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  • 2011-03-15. Split Monotone Variational Inclusions in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 2013-06-08. A Levenberg-Marquardt method with approximate projections in COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
  • 2016-10-31. A new class of nonmonotone adaptive trust-region methods for nonlinear equations with box constraints in CALCOLO
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  • 2014-07-02. A Relaxed Projection Method for Split Variational Inequalities in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 2014. Implicit Functions and Solution Mappings, A View from Variational Analysis in NONE
  • 1994-03. Local analysis of Newton-type methods for variational inequalities and nonlinear programming in APPLIED MATHEMATICS & OPTIMIZATION
  • 2011-08-05. Algorithms for the Split Variational Inequality Problem in NUMERICAL ALGORITHMS
  • 2013-03-26. Convergence of inexact Newton methods for generalized equations in MATHEMATICAL PROGRAMMING
  • 2013-10-30. Local convergence of quasi-Newton methods under metric regularity in COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
  • 1996-06. Generalized equations and the generalized Newton method in MATHEMATICAL PROGRAMMING
  • 2001. An Active Set-Type Newton Method for Constrained Nonlinear Systems in COMPLEMENTARITY: APPLICATIONS, ALGORITHMS AND EXTENSIONS
  • 1973-10. Newton's method for nonlinear inequalities in NUMERISCHE MATHEMATIK
  • 2011-09-06. Common Solutions to Variational Inequalities in SET-VALUED AND VARIATIONAL ANALYSIS
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    http://scigraph.springernature.com/pub.10.1007/s10589-018-0040-0

    DOI

    http://dx.doi.org/10.1007/s10589-018-0040-0

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