A Hybrid Steepest-descent Scheme for Convex Minimization over Optimization Problems

Authors

  • Yasir Arfat King Mongkut’s University of Technology Thonburi (KMUTT) https://orcid.org/0000-0001-8314-3602
  • Ihsan Ul Ghafoort University of Gujrat
  • Yeol Je Cho Department of Mathematics, Education Gyeogsang National University, Jinju, South Korea.

DOI:

https://doi.org/10.58715/ncao.2023.2.4

Keywords:

Hybrid steepest descent method, Convex minimization problem, Equilibrium problem, Variational inequality problem, Fixed point problem

Abstract

Within the context of Hilbert spaces, we demonstrate the robust convergence of a hybrid steepest-descent approximant towards a solution for a convex minimization problem. This problem is situated within the space of solutions for equilibrium problems and the fixed point set of a finite family of η-demimetric operators. Additionally, we present numerical results that shed light on the effectiveness of the proposed approximants, offering insights into potential applications.

Author Biographies

Yasir Arfat, King Mongkut’s University of Technology Thonburi (KMUTT)

B.Sc. M.Sc. and PhD. in Mathematics

Ihsan Ul Ghafoort, University of Gujrat

Faculty of Science, Department of Mathematics, University of Gujrat, Gujrat, 50700, Pakistan.

Yeol Je Cho, Department of Mathematics, Education Gyeogsang National University, Jinju, South Korea.

Professor in Mathematics at the Department of Mathematics, Education Gyeogsang National University, Jinju, South Korea.

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Published

2023-12-30

How to Cite

Arfat, Y., Ghafoort, I. U., & Cho, Y. J. (2023). A Hybrid Steepest-descent Scheme for Convex Minimization over Optimization Problems. Nonlinear Convex Analysis and Optimization: An International Journal on Numerical, Computation and Applications, 2(2), 75–91. https://doi.org/10.58715/ncao.2023.2.4

Issue

Vol. 2 No. 2 (2023): July - December, 2023

Section

Articles

License

Copyright (c) 2023 Yasir Arfat, Ihsan Ul Ghafoort, Yeol Je Cho

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