Asymptotic Analysis And Confidence Solution Estimation For Two Kinds Of Stochastic Programming Problems

Since it reflects the uncertain factors that occur in practice,the problem of stochastic equilibrium problem and stochastic conic programming which have draw much attention by many scholars recently.It is widely used in many fields such as economics,engineering,management engineering,etc.People usually combine approximate methods to solve random models with expected values.Such methods require the asymptotic theory of random programming to ensure.However,most asymptotic theory focus on the convergence of the approximation problem with probability one for true problems,and pay less attention to the convergence in distribution of the approximation problem.In fact,the result of convergence in distribution ensures the theoretical of obtaining a confidence solution to the true problem.This paper studies the convergence in distribution of one-stage stochastic linear complementarity problem and approximation problem of stochastic second-order cone programming problems.The main contents of this article are as follows:Firstly,the research background and current situation of one stage stochastic linear complementarity problem and stochastic second-order cone programming problem are introduced.Secondly,we study the asymptotic convergence of the estimator of the sample average approximation problem of stationary point condition of the stochastic inequality constrained optimization problem.Then we apply the results to the stochastic linear complementarity problem,obtain the conditions which ensure the asymptotic normality of the estimator of the approximation problem,and obtain the method to estimate the confidence region of the true solution.Thirdly,by the perturbation analysis of the second-order cone programming,the consistency of the approximation problem is obtained,and the asymptotic convergence of the estimator of the sample average approximation problem of the stochastic second-order cone programming are established.Thus,the conditions ensuring the asymptotic normality of the sample average approximation stationary point of the stochastic second-order cone programming are obtained,and the method for estimating the confidence region of the true optimal solution of the stochastic second-order cone programming is obtainedFinally,based on the established asymptotic theory,the confidence regions for estimating the ture solutions of one-stage stochastic linear complementarity problems andstochastic second-order cone programming problems are obtained by numerical experiments,which verify the effectiveness of the method.