A conjugate gradient projection method for solving equations with convex constraints

Abstract In this paper, we propose a derivative-free iterative method for a class of equations with convex constraints appearing in a variety of the practical problems such as compressing sensing, fluid mechanics, plasma physics, nonlinear optics and solid state. In the iteration, our search direction can be viewed as an extension of a modified three-term CG method. By an appropriate line search and the projection step, our method is convergent to the solution. Our method inherits the advantages of CG method and projection method, and thus is suitable for solving large-scale non-smooth problem. Under the assumption that F is Lipschitz continuous and satisfies a weaker condition of monotonicity, our method is globally convergent. Numerical results show the efficiency of the proposed method.