Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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A THREE-TERM INERTIAL DERIVATIVE-FREE PROJECTION METHOD FOR CONVEX CONSTRAINED MONOTONE EQUATIONS

  • Noinakorn, Supansa (Mathematics and Computing Science Program, Faculty of Science and Technology Phetchabun Rajabhat University) ;
  • Ibrahim, Abdukarim Hassan (KMUTTFixed Point Research Laboratory, Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT)) ;
  • Abubakar, Auwal Bala (Department of Mathematical Sciences, Faculty of Physical Sciences Bayero University Kano) ;
  • Pakkaranang, Nuttapol (Mathematics and Computing Science Program, Faculty of Science and Technology Phetchabun Rajabhat University)
  • Received : 2021.05.06
  • Accepted : 2021.11.02
  • Published : 2021.12.15
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Abstract

Let 𝕽n be an Euclidean space and g : 𝕽n → 𝕽n be a monotone and continuous mapping. Suppose the convex constrained nonlinear monotone equation problem x ∈ 𝕮 s.t g(x) = 0 has a solution. In this paper, we construct an inertial-type algorithm based on the three-term derivative-free projection method (TTMDY) for convex constrained monotone nonlinear equations. Under some standard assumptions, we establish its global convergence to a solution of the convex constrained nonlinear monotone equation. Furthermore, the proposed algorithm converges much faster than the existing non-inertial algorithm (TTMDY) for convex constrained monotone equations.

Keywords

Acknowledgement

The first and fourth authors would like to thank Phetchabun Rajabhat University. The third author acknowledge with thanks, the Department of Mathematics and Applied Mathematics at the Sefako Makgatho Health Sciences University.

References

  1. A.B. Abubakar, P. Kumam, M. Malik, P. Chaipunya, and A.H. Ibrahim, A hybrid fr-dy conjugate gradient algorithm for unconstrained optimization with application in portfolio selection, AIMS Mathematics, 6(6) (2021), 6506-6527. https://doi.org/10.3934/math.2021383
  2. A.B. Abubakar, P. Kumam, M. Malik, and A.H. Ibrahim, A hybrid conjugate gradient based approach for solving unconstrained optimization and motion control problems, Math. Comput. Simul., (2021), doi.org/10.1016/j.matcom.2021.05.038.
  3. A.B. Abubakar, P. Kumam, A.H. Ibrahim, and J. Rilwan, Derivative-free hs-dy-type method for solving nonlinear equations and image restoration, Heliyon, 6(11):e05400, (2020), doi.org/10.1016/j.heliyon.2020.e05400.
  4. A.B. Abubakar, K. Muangchoo, A.H. Ibrahim, A.B. Muhammad, L.O. Jolaoso, and K.O. Aremu, A new three-term hestenes-stiefel type method for nonlinear monotone operator equations and image restoration, IEEE Access, 9 (2021), 18262-18277. https://doi.org/10.1109/ACCESS.2021.3053141
  5. A.B. Abubakar, K. Muangchoo, A.H. Ibrahim, J. Abubakar, and S.A. Rano, Fr-type algorithm for finding approximate solutions to nonlinear monotone operator equations, Arabian J. Math., 10 (2021), 261-270. https://doi.org/10.1007/s40065-021-00313-5
  6. A.B. Abubakar, P. Kumam, H. Mohammad, and A.H. Ibrahim, Prp-like algorithm for monotone operator equations, Japan J. Indus. Appl. Math., 38 (2021), 805-822. https://doi.org/10.1007/s13160-021-00462-2
  7. A.B. Abubakar, K. Muangchoo, A.H. Ibrahim, S.E. Fadugba, K.O. Aremu, and L.O. Jolaoso, A modified scaled spectral- conjugate gradient-based algorithm for solving monotone operator equations, J. Math., 2021 (2021), doi.org/10.1155/2021/5549878.
  8. A.B. Abubakar, P. Kumam, and A.H. Ibrahim, Inertial derivative-free projection method for nonlinear monotone operator equations with convex constraints, IEEE Access, 9 (2021), 92157-92167. https://doi.org/10.1109/ACCESS.2021.3091906
  9. A.B. Abubakar, P. Kumam, A.H. Ibrahim, P. Chaipunya, and S.A. Rano, New hybrid three-term spectral-conjugate gradient method for finding solutions of nonlinear monotone operator equations with applications, Math. Comput. Simul., (2021). doi.org/10.1016/j.matcom.2021.07.005.
  10. J. Abubakar, P. Kumam, A.H. Ibrahim, and A. Padcharoen, Relaxed inertial tseng's type method for solving the inclusion problem with application to image restoration, MDPI Mathematics, 8(5) (2020),818. doi.org/10.1016/j.matcom.2021.07.005.
  11. J. Abubakar, P. Kumam, H.ur Rehman and A.H. Ibrahim, Inertial iterative schemes with variable step sizes for variational inequality problem involving pseudomonotone operator, MDPI Mathematics, 8(4) (2020), 609. doi.org/10.3390/math8040609.
  12. H. Cao, A three-term derivative-free projection method for convex constrained monotone equations, ScienceAsia, 47(2) (2021), 235-240. https://doi.org/10.2306/scienceasia1513-1874.2021.018
  13. S.P. Dirkse and M.C. Ferris, Mcplib: A collection of nonlinear mixed complementarity problems, Optimi. Meth. Software, 5(4) (1995), 319-345. https://doi.org/10.1080/10556789508805619
  14. E.D. Dolan and J.J. More, Benchmarking optimization software with performance profiles. Math. Programming, 91(2) (2002), 201-213. https://doi.org/10.1007/s101070100263
  15. P. Gao and C. He, An efficient three-term conjugate gradient method for nonlinear monotone equations with convex constraints, Calcolo, 55 (2018), Article number: 53. doi.org/10.1007/s10092-018-0291-2
  16. A.H. Ibrahim, A.I. Garba, H. Usman, J. Abubakar and A.B. Abubakar, Derivative-free rmil conjugate gradient method for convex constrained equations, Thai J. Math., 18(1) (2020), 211-231.
  17. A.H. Ibrahim, P. Kumam, A.B. Abubakar, W. Jirakitpuwapat and J. Abubakar, A hybrid conjugate gradient algorithm for constrained monotone equations with application in compressive sensing, Heliyon, 6(3) (2020), e03466. doi: 10.1016/j.heliyon.2020.e03466.
  18. A.H. Ibrahim, P. Kumam, A.B. Abubakar, J. Abubakar and A.B. Muhammad, Least-square-based three-term conjugate gradient projection method for ℓ1-norm problems with application to compressed sensing, MDPI Mathematics, 8(4) (2020):602. doi.org/10.3390/math8040602.
  19. A.H. Ibrahim, P. Kumam, A.B. Abubakar, U.B. Yusuf and J. Rilwan. Derivative-free conjugate residual algorithms for convex constraints nonlinear monotone equations and signal recovery, J. Nonlinear Convex Anal., 21 (2020), 1959-1972.
  20. A.H. Ibrahim, P. Kumam and W. Kumam, A family of derivative-free conjugate gradient methods for constrained nonlinear equations and image restoration, IEEE Access, 8 (2020), 162714-162729. https://doi.org/10.1109/access.2020.3020969
  21. A.H. Ibrahim, P. Kumam, A.B. Abubakar, U.B. Yusuf, S.E. Yimer and K.O. Aremu,An efficient gradient-free projection algorithm for constrained nonlinear equations and image restoration, AIMS Mathematics, 6(1) (2020), 235-260. doi: 10.3934/math.2021016.
  22. A.H. Ibrahim, K. Muangchoob, N.S. Mohamed and A.B. Abubakar, Derivative-free smr conjugate gradient method for constraint nonlinear equations, J. Math. Comput. Sci., 24(2) (2022),147-164.
  23. A.H. Ibrahim, K. Muangchoo, A.B. Abubakar, A.D. Adedokun and H. Mohammed, Spectral conjugate gradient like method for signal reconstruction, Thai J. Math., 18(4) (2020), 2013-2022.
  24. A.H. Ibrahim and P. Kumam, Re-modified derivative-free iterative method for nonlinear monotone equations with convex constraints, Ain Shams Eng. J., (2021). doi.org/10.1016/j.asej.2020.11.009.
  25. A.H. Ibrahim, J. Deepho, A.B. Abubakar and K.O. Aremu, A modified liu-storeyconjugate descent hybrid projection method for convex constrained nonlinear equations and image restoration, Num. Algebra Control Opti., (2021). doi: 10.3934/naco.2021022
  26. A.H. Ibrahim, P. Kumam, B.A. Hassan, A.B. Abubakar and J. Abubakar, A derivative-free three-term hestenes-stiefel type method for constrained nonlinear equations and image restoration, Inter. J.Comput. Math., (2021), 1-22. doi.org/10.1080/00207160.2021.1946043
  27. A.H. Ibrahim, J. Deepho, Auwal Bala Abubakar and A. Adamu, A three-term polakribire-polyak derivative-free method and its application to image restoration, Scientific African, 13 (2021), e00880. doi.org/10.1016/j.sciaf.2021.e00880.
  28. A.H. Ibrahim, P. Kumam, M. Sun, P. Chaipunya and A.B. Abubakar, Projection method with inertial step for nonlinear equations: Application to signal recovery, J. Indus.Manag. Optimi., (2021). doi: 10.3934/jimo.2021173
  29. C. Izuchukwu and Y. Shehu, New inertial projection methods for solving multivalued variational inequality problems beyond monotonicity, Networks Spatial Econo., 22(2) (2021), 291-323. doi: 10.1007/s11067-021-09517-w
  30. C. Izuchukwu, S. Reich, and Y. Shehu, Relaxed inertial methods for solving the split monotone variational inclusion problem beyond co-coerciveness, Optimization., (2021), 1-40. doi.org/10.1080/02331934.2021.1981895
  31. K. Meintjes and A.P. Morgan, A methodology for solving chemical equilibrium systems, Appl. Math. Comput., 22(4) (1987), 333-361. https://doi.org/10.1016/0096-3003(87)90076-2
  32. B.T. Polyak, Some methods of speeding up the convergence of iteration methods, Ussr Comput. Math. Math. Physics, 4(5) (1964), 1-17. https://doi.org/10.1016/0041-5553(64)90137-5
  33. M.V. Solodov and B.F. Svaiter, A new projection method for variational inequality problems, SIAM J. Cont. Optimi., 37(3) (1999), 765-776. https://doi.org/10.1137/S0363012997317475
  34. A.J. Wood and B.F. Wollenberg, Power generation, operation and control, New York: John Wiley & Sons, 1996.
  35. Y. Xiao and H. Zhu, A conjugate gradient method to solve convex constrained monotone equations with applications in compressive sensing, J. Math. Anal. Appl., 405(1) (2013), 310-319. https://doi.org/10.1016/j.jmaa.2013.04.017