A method with inertial extrapolation step for convex constrained monotone equations View Full Text


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Article Info

DATE

2021-12-06

AUTHORS

Abdulkarim Hassan Ibrahim, Poom Kumam, Auwal Bala Abubakar, Jamilu Abubakar

ABSTRACT

In recent times, various algorithms have been incorporated with the inertial extrapolation step to speed up the convergence of the sequence generated by these algorithms. As far as we know, very few results exist regarding algorithms of the inertial derivative-free projection method for solving convex constrained monotone nonlinear equations. In this article, the convergence analysis of a derivative-free iterative algorithm (Liu and Feng in Numer. Algorithms 82(1):245–262, 2019) with an inertial extrapolation step for solving large scale convex constrained monotone nonlinear equations is studied. The proposed method generates a sufficient descent direction at each iteration. Under some mild assumptions, the global convergence of the sequence generated by the proposed method is established. Furthermore, some experimental results are presented to support the theoretical analysis of the proposed method. More... »

PAGES

189

References to SciGraph publications

  • 2017-03-06. A spectral algorithm for large-scale systems of nonlinear monotone equations in NUMERICAL ALGORITHMS
  • 2021-03-01. Inertial methods for finding minimum-norm solutions of the split variational inequality problem beyond monotonicity in NUMERICAL ALGORITHMS
  • 2018-09-11. An improved three-term derivative-free method for solving nonlinear equations in COMPUTATIONAL AND APPLIED MATHEMATICS
  • 2018-09-25. A derivative-free iterative method for nonlinear monotone equations with convex constraints in NUMERICAL ALGORITHMS
  • 2005-04. Superlinear Convergence of a Newton-Type Algorithm for Monotone Equations in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 2002-01. Benchmarking optimization software with performance profiles in MATHEMATICAL PROGRAMMING
  • 2021-02-17. FR-type algorithm for finding approximate solutions to nonlinear monotone operator equations in ARABIAN JOURNAL OF MATHEMATICS
  • 2001-03. An Inertial Proximal Method for Maximal Monotone Operators via Discretization of a Nonlinear Oscillator with Damping in SET-VALUED AND VARIATIONAL ANALYSIS
  • 2019-07-08. A Dai–Liao conjugate gradient method via modified secant equation for system of nonlinear equations in ARABIAN JOURNAL OF MATHEMATICS
  • 2021-02-18. PRP-like algorithm for monotone operator equations in JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS
  • 2020-04-13. Descent Perry conjugate gradient methods for systems of monotone nonlinear equations in NUMERICAL ALGORITHMS
  • 2018-05-12. A descent Dai-Liao conjugate gradient method for nonlinear equations in NUMERICAL ALGORITHMS
  • 1999. A Logarithmic-Quadratic Proximal Method for Variational Inequalities in COMPUTATIONAL OPTIMIZATION
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    URI

    http://scigraph.springernature.com/pub.10.1186/s13660-021-02719-3

    DOI

    http://dx.doi.org/10.1186/s13660-021-02719-3

    DIMENSIONS

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