Abstract: This paper presents a modified hybrid three-term conjugate gradient projection method (MHTTCGPM) for solving large-scale nonlinear monotone equations with convex set constraints. The method incorporates an adaptive line search technique, ensuring that the search direction satisfies the sufficient descent property. Without requiring Lipschitz continuity, the global convergence of the proposed method is rigorously established. Numerical results demonstrate the effectiveness and reliability of the new algorithm.

Key words: Nonlinear monotone equations, Three-term conjugate gradient, Global convergence, Line search technique, Convex set constraint