A Modified Hestenes-Stiefel Type Method for Finding an Approximate Solution of Nonlinear Monotone Equations - Yusuf, Aliyu; Eshiokhe, Paul Victor (FUDMA Journal of Sciences, 2026)
This research presents a Modified Hestenes-Stiefel (HS) conjugate gradient method for solving systems of monotone equations. A modified Hestenes-Stiefel (MHS) type method designed to efficiently obtain approximate solutions for monotone equations. The paper introduces an innovative three-term derivative-free projection algorithm based on a modified Hestenes-Stiefel (MHS) parameter for solving nonlinear monotone equations. The proposed algorithm is designed to be effective, derivative-free, and exhibits low memory requirements, making it particularly suitable for large-scale problems. A key feature of the algorithm is its ability to generate bounded descent search directions at each iteration, independent of the line search procedures. Under standard assumptions, we establish the global convergence properties of the method. Comprehensive numerical experiments demonstrate the efficiency of the algorithm in handling large-scale nonlinear monotone equations. Preliminary numerical experiments indicate that the propose method is promising and competitive with existing techniques for solving monotone equations. The promising results suggest that the MHS method is a viable and efficient alternative for solving a wide range of monotone equations.
Keywords: Derivative-free Method; Nonlinear Monotone Equations; Projection Method; Global Convergence; Numerical Experiments; Signal Recovery Problems