Modified Dai-Yuan Conjugate Gradient Method with Sufficient Descent Property for Nonlinear Equations

The convex constraint nonlinear equation problem is to find a point q with the property that q is an element of D, where D is a nonempty closed convex subset of Euclidean space R-n. The convex constraint problem arises in many practical applications such as chemical equilibrium systems, economic equilibrium problems, and the power flow equations. In this paper, we extend the modified Dai-Yuan nonlinear conjugate gradient method with sufficiently descent property proposed for large-scale optimization problem to solve convex constraint nonlinear equation and establish the global convergence of the proposed algorithm under certain mild conditions. Our result is a significant improvement compared with related method for solving the convex constraint nonlinear equation.