Optimality Conditions For Two-stage Stochastic Second-order Cone Programming Problems

Optimization problems involving stochastic models occur in almost all areas of science and engineering.Therefore,research on theoretical analysis and solutions of stochastic problems has attracted more attention of scholars at home and abroad.In recent years,significant progress has been made in solving two-stage stochastic programming problems.For example,primal-dual decomposition algorithm based on interior point method can effectively solve the two-stage stochastic linear programming problem.With the development of society,many important practical problems,such as the optimal scheduling problem of power systems with new energy,signal emission intensity processing,and so on,can be modeled as a two-stage stochastic second-order cone programming problem.Study of effective solutions to this type of problem is a subject of great theoretical significance and practical value.As we all know,optimality conditions play an important role in algorithm design.Based on Lagrange duality theory and the sub-differential property of the function,this thesis mainly discussed the optimality conditions of the two-stage stochastic second-order cone programming problem when random data follow discrete distribution and general distribution respectively.The main research contents are as follows:Chapter 1 introduced the research status of stochastic second-order cone programming problem,two-stage stochastic programming problem,and two-stage stochastic second-order cone programming problem.Preliminary knowledge related to research was also introduced.In chapter 2,under the Slater constraint qualification,Lagrange duality problem for stochastic second-order cone programming problems was established based on the second-order cone duality theory.And sub-differential property of the optimal value function Q(x,?)was analyzed.Chapter 3 discussed the two-stage stochastic second-order cone programming problem with a discrete distribution of the random data.Firstly,the sub-differential property of the expected compensation function(36)[Q(x,?)] was discussed;Secondly,based on the duality theory,optimality conditions for the two-stage stochastic second-order cone programming problem was proved.Chapter 4 discussed the two-stage stochastic second-order cone programming problem with a general distribution of the random data.Firstly,under certain assumptions,the sub-differential property of the expected compensation function(36)[Q(x,?)] was discussed;Secondly,based on the duality theory,optimality conditions for the two-stage stochastic second-order cone programming problem was proved;Finally,the sample average approximation problem of the two-stage stochastic second-order cone programming problem was built and convergence of sample average approximation estimators was proved.