Study On Modified Augmented Lagrangian Method For Solving Convex Optimization Problems

The classical augmented Lagrangian method is an effective method(ALM)for solving convex optimization problems with linear equality constraints.However,the efficiency of the ALM depends highly on the computational efforts on solving the xsubproblems.For some convex optimization problems,the efficiency of the ALM can be greatly improved by introducing a relaxation factor in the dual step.In this thesis,we linearize the objective function in the augmented Lagrangian function for solving the x-subproblem to derive a new algorithm,called the modified augmented Lagrangian method(MALM),and establish its global convergence under special conditions.What's more,we introduce a relaxation factor to get a faster MALM.We also apply the MALM to some concrete examples,and compare with some existing algorithms to verify the efficiency of the MALM.