Relaxed Augmented Lagrangian Method For Convex Optimization Problems With Linear Constraints

The augmented Lagrangian method(ALM)is a classical method for solving con-vex optimization problems with linear constraints.It has been found that for some con-vex optimization problems with a large amount of computation or a favorable structure,slack factors can be introduced to shrink Lagrangian multipliers,that is,the relaxed ALM.Using this method to solve the problem,can basically get a closed form solution with a global convergence,but the relaxed factor only takes value within(0,2).Based on the relaxed ALM,this paper extends the value range of its relaxed factor for the con-vex optimization model with linear constrained.It is proved that when the objective function is a strong convex function,the relaxed factor can be in a larger interval con-taining(0,2)and guarantee the global convergence of the algorithm at the same time.Finally,the numerical results verify the effectiveness of the extended range of the re-laxation factor,and compared with other algorithms,the required number of iterations is significantly reduced under the same relative error.