A Relaxed Alternating Directions Of Multipliers Method For Convex Programming

As we all know, convex programming problems with separable structure are a class of important constraint optimization problems. The alternating directions method of multipliers is one of the important methods for these problems. It is a demposition algorithm, which obtains the solution to the primal problem via solving a lot of subproblems. The alternating directions method of multipliers was proposed by Glowinski and Marroco and by Gabay and Merrier.In this paper, we give a relaxed alternating directions method of multipliers, which is based on the alternating directions method of multipliers and the proximal method of multipliers. There are two differenences between the relaxed alternating directions method of multipliers and the above two methods.1.At each itcration,the algorithm computesλtwice.2.The algorithm introduces a relaxation factorγ.So, the algorithm not only takes advantage of the structure of the problem, but also converges provided that f and g are convex functions. Furthermore, the introducation of a relaxation factor makes the algorithm has a wide range of uses.In the second chapter, we give the relaxed alternating directions method of multipliers. In the third chapter, we prove convergence of the algorithm.And we give three examples in the fourth chapter.