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 2 D where D is a nonempty closed convex subset of Euclidean space Rⁿ. 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 su ciently 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.