Derivative-free restrictively preconditioned conjugate gradient path method without line search technique for solving linear equality constrained optimization

In this paper, we propose a derivative-free restrictively preconditioned conjugate gradient path method without line search technique for solving linear equality constrained optimization. This method originates from the classical conjugate gradient method and its restrictively preconditioned variant. The preconditioned conjugate gradient path is obtained by solving extended system of the preconditioned equation with restrictively preconditioned conjugate gradient method which is a more robust and effective technique to solve large sparse linear system. The global convergence and local superlinear convergence rate of the proposed method are established under some reasonable conditions. Finally, the numerical results are reported to show the effectiveness of the proposed method.