Research On Two-stage Stochastic Second-order Cone Programming Problem With Recourse

Second-order cone programming(SOCP)is a kind of convex optimization problem.In order to deal with the uncertainty of data in SOCP,two-stage stochastic second-order cone programming problem with compensation has become a hot topic of research.Such as stochastic Euclidean facility location problem,portfolio optimization problem with loss risk constraint,optimal coverage random ellipsoid problem,etc.The effective solution method mostly focuses on interior point method.Based on the theory and algorithm of two-stage stochastic linear programming,this paper mainly discusses two-stage stochastic second-order cone with compensation.Under the condition of Slater constraint specification,the dual problem of the second stage problem and the subdifferential property of the optimal value function are discussed.Under the condition that the probability distribution of the random variable has finite support,The theory and algorithm of the two-stage random second-order cone are studied.The main results of this paper are as follows:The first chapter introduces the research background and current situation of second-order cone programming and random second-order cone programming.The second chapter introduces the theory and algorithm of two-stage stochastic linear programming.Firstly,the two-stage stochastic linear programming model with compensation constraints is introduced.Secondly,the equivalent problem of two-stage stochastic linear optimization problems with discrete distribution is given,and optimality conditions is also presented;Finally,the logarithmic barrier interior method for solving two-stage stochastic linear optimization problems is introduced.In the third chapter,the two-stage stochastic second-order cone programming problem with compensation is studied.Firstly,the two-stage stochastic second-order cone programming model with compensation is given.Secondly,the dual problem and optimal value function of the second-stage problem are discussed.The differential property of the function is described.An equivalent problem for the two-stage stochastic optimization problem with discrete distribution is given,and the optimality condition of the equivalence problem is analyzed.Finally,basic idea of logarithmic barrier interior point method for solving the two-stage stochastic second-order cone programming problem is introduced.