A Three-Term Hybrid Conjugate Gradient Projection Method for Solving Convex Constrained Nonlinear Monotone Equations and Applications

This paper presents a new three-term hybrid conjugate gradient projection method for handling large-scale convex-constrained nonlinear monotone equations that are prevalent in fields such as engineering optimization, data science, and signal processing. This method is based on a three-term conjugate gradient approach, that combines hybrid and projection techniques. A key advantage is that the search direction of the proposed method satisfies sufficient descent and trust region properties, which are not dependent on the line search technique. Under the specified conditions, the method achieves global convergence. Numerical experiments contrasted the proposed method with the other two approaches, demonstrating its reliability and robustness in terms of the iteration number, function evaluation number, and CPU running time. This method has been applied to sparse-signal recovery problems. The CPU running time, number of iterations, and mean squared error of the proposed method are superior to those of the other two methods, further verifying its applicability and effectiveness. Finally, possible future research directions for this method were proposed.