(untitled) (European Journal of Pure and Applied Mathematics, 2025)
Because of their computing efficiency and minimal memory requirements, conjugate gradient techniques are a fundamental family of algorithms for handling large-scale unconstrained nonlinear optimization problems. A new version of the Hestenes-Stiefel (HS) technique is presented in this study with the goal of improving convergence properties without compromising ease of use. We rigorously prove the global convergence qualities of the proposed approach under standard assumptions and show that it meets the conjugacy, descent, and adequate descent constraints. Numerous numerical tests, covering a wide range of benchmark issues, show that the suggested strategy routinely performs better than the traditional HS approach in terms of function evaluations and iteration count.