Mirror Descent SA Algorithm For Solving Least Squares Problem

The least squares problem is widely used in the fields of physics,statistics and economy.It is of great help to data prediction and error estimation.It is of practical significance to study the problem.At present,there are many effective algorithms to solve the least squares problem,such as Schmidt orthogonal method,penalty function method,Newton method and so on,The mirror descent SA algorithm has a good convergence rate in solving a class of convex stochastic programming problems.Therefore,this paper applies the mirror descent SA algorithm to solve the stochastic least squares problems and analyzes the convergence of the algorithm,An example is given to illustrate the feasibility of the algorithm.Other solutions to the stochastic least squares problem are introduced and compared with the mirror descent SA algorithm.In the first chapter of this paper,we mainly introduce the research background and current situation of least square problem,stochastic programming problem,mirror descent SA algorithm and sample mean approximation method.In the second chapter,we introduce the preparatory knowledge needed in this paper.In the third chapter,we describe the main structure of the mirror descent SA algorithm combined with the development of the algorithm.In the fourth chapter,the form of stochastic least squares problem is introduced,and the mirror descent SA algorithm is used to solve the problem.The convergence of the algorithm is proved,and the convergence rate is discussed.The MATLAB program is used to solve the given example,and compared with the distributed robust optimization method.Finally,the full text is summarized and the conclusion is described.