Research On Alternating Direction Multiplier Method Of Coupling Of Objective Function

Optimization has been an important branch of operations research,but also plays an important role in other aspects.Nowadays,the application of image processing and digital signal is a problem to be solved by optimization algorithm.Therefore,how to study the efficient algorithm is the main content of the research.For the problem of objective function separability with linear constraints,many mature algorithms have been developed,such as augmented lagrange multiplier method,custom proximal point algorithm and block-wise alternating direction method of multipliers with multi-block variables.However,there is little research on the coupling of objective function.Such problems are likely to arise in the provision of wireless networks and smart grid provisioning.This paper talks about solving multi-block convex optimization problems with linear constraints,among which is the inseparable term of object function.For cases where there are inseparable terms in the objective function,we first discussed the problem of coupling terms in two pieces,the method of alternating proximal gradient method of multipliers,alternating gradient projection method of multipliers,and the hybrids thereof are introduced to solve the problem.When the coupling term extends to multiple variables,Chao miantao et al.have proposed a PBMM-MS algorithm[1] by integrating block coordinate descent method with alternating direction method of multipliers,and verified its validity via numerical experiments.When the objective may have a nonseparable quadratic term and separable nonsmooth terms,we introduce a hybrid Jacobian and Gauss – Seidel BCU method for solving linearly constrained multiblock structured convex programming[18] and the convergence of the algorithm is proved.The innovation of this paper is to improve PBMM-MS algorithm,we propose a new algorithm to be called proximal block multiplier minimization algorithm with adaptive step size and substitution procedure.The algorithm adopts the adaptive step size technique that enables auto-matical adjustment of the step size during the iterative process.Hence,the computational efficiency of the algorithm is improved.The specific research content of this article is arranged as follows:The first chapter is the introduction,which mainly introduces the background and research significance of the topic,as well as the current status of domestic and foreign research.In the second chapter,for the case where the objective function is separable,it is solved by augmented Lagrangian algorithm,customized PPA algorithm,and constrained separable alternating direction method of multipliers under multiple variables.Chapter three,When the coupling term exists in the objective function,thecorresponding algorithm is introduced to solve it.In the fourth chapter,in the case of objective function coupling,introduces proximal block multiplier minimization algorithm with adaptive step size and substitution procedure,and solve with step-size adaptive adjustment technique.