Asymptotic Analysis Of A Class Of Stochastic Second-Order Cone Programming Problems

Stochastic programming reflects the potential uncertainty in practical problems such as economy,finance,engineering and management.It has become one of the most potential directions in the field of mathematical optimization.In recent years,with the application of stochastic programming model in more fields,new stochastic optimization models are emerging.Recently,as a new stochastic programming model,stochastic second-order cone programming has attracted much attention.It provides a unified research form for practical problems such as optimal location problem,manipulator grasp problem in uncertain environment and so on.The theoretical premise of using approximate method to solve stochastic second-order cone programming with expected value is the asymptotic analysis of stochastic second-order cone programming,so the establishment of asymptotic analysis of stochastic second-order cone programming has important theoretical and application value.In this paper,we establish the estimation formula of the sample mean approximation problem for stochastic second-order cone programming problems.Based on the asymptotic analysis of convergence according to distribution,we apply it to practical problems and expand the theory and application of asymptotic analysis for stochastic second-order cone programming problems.This paper is divided into three parts.Firstly,the research background is introduced in the first chapter,including the research background of stochastic programming,deterministic second-order cone programming and stochastic second-order cone programming.Secondly,in the second chapter,the asymptotic analysis theory of the approximate estimation of the sample mean for the stochastic second-order cone programming problem is established.In this paper,we obtain the condition that the approximate estimator of sample mean converges to multivariate normal distribution according to distribution,and describe the concrete form of correlation covariance matrix.The results extend the existing asymptotic analysis of stochastic programming problems with equality and inequality constraints to stochastic programming problems with second-order cone constraints.Thirdly,in the third chapter,a method to estimate the confidence interval of the real optimal solution of the stochastic second-order cone programming problem is proposed by using the results of the second chapter,and an example is given to illustrate how to verify the conditions in the theorem and obtain the confidence region.Finally,in the fourth chapter,the results of the first two chapters are applied to the grasping force problem and the random location problem of the manipulator in the random environment.Through numerical experiments,the confidence region of the real optimal solution of the stochastic second-order cone programming problem is obtained.