A Family of Projection-Based Spectral Conjugate Gradient Algorithm for Constrained Monotone Nonlinear Equations with Application

Finding the solution to constrained monotone nonlinear equations has become more challenging as the number of dimensions rises. In this paper, a projection-based spectral conjugate gradient algorithm for solving monotone nonlinear equations with convex constraints is proposed. This algorithm features two bounded spectral parameters designed by using the quasi-Newton condition and the double-truncating technique. An improved conjugate parameter ensures that the search direction satisfies the sufficient descent and trust-region properties. The global convergence of the algorithm is established under reasonable assumptions. Numerical experiments demonstrate that it is promising and robust for large-scale nonlinear equations with convex constraints in both fixedly and randomly initial point strategies, as well as for the sparse signal reconstruction problem.