An extension of the Fletcher–Reeves method to linear equality constrained optimization problem

In this paper, combining the feasible direction method with the conjugate gradient method, we propose a feasible Fletcher–Reeves conjugate gradient method for solving linear equality constrained optimization problem. The directions generated by the method are feasible and descent for the objective function. Under mild conditions, we show that the proposed method with exact line search is globally convergent. Numerical experiments are also given to show the efficiency of the method.