Rosen's gradient projection method for solving a constrained convex programming problem

Abstract

When the classical Rosen’s method is applied to solving the dual of a convex programming problem, calculating the projection gradient direction at each iteration involves solving a minimization problem of Lagrangian function. By employing any parallel algorithms, an approximate solution can be obtained, which can approach any accuracy of the optimal solution. It is illustrated that, if the sequence of accuracies are properly chosen, the value of the dual variable at the -th iterate, generated by the modified Rosen’s method, converges to the optimal solution to the dual problem and the generated sequence also converges to the optimal solution to the original convex programming problem.