A New Model Of Stochastic Symmetry Cone Complementarity Problems And Their Solving Method

Symmetric Cone Complementarity Problems(SCCP)are one classes of equilibrium optimization problems which is rich in theory,novel in content and broad in coverage.it is widely used in transportation,economy,countermeasure theory,engineering mechanics and many other fields,however,many stochastic factors are often encountered during application,such as weather changes,supply chain demand,market turbulence,etc.At present,researchers used Euclidean Jordan algebraic techniques and spectral factorization theorem to obtain a lot of important results in researching the related fields of Stochas-tic Second-Order Cone Complementarity Problems(SSOCCP),however,the research on the stochastic form of symmetric cones complementarity prolblems is relatively lacking.Therefore,the research on Stochastic Sylmetric Cone Complementarity Problems(SS-CCP)is worth exploring either from its theoretical research value or from its practical application.This paper presents the Conditional Value-at-Risk(CVaR)model for solving the problem of SSCCP,the research content mainly includes the following aspects:The first chapter gives a brief overview of the source and background of the com-plementary problems,and then introduces the concepts of SSCCP and the SSCCP with stochastic parameters;The second chapter introduces the relevant preliminary knowledge,mainly explains the basic concepts and related knowledge involved in the following content,it specifically includes relevant symbols and definitions,the Euclidean Jordan algebraic and Spectral Factorization theorem,the CVaR model,the Sample Average Approximation method,Symmetric Cone Complementary Function,etc;In the third chapter,the CVaR model for solving SSCCP is firstly given based on the value-at-Risk(VaR),and the boundedness of the level set is proved theoretically.Sec-ondly,since the objective function of the CVaR model is non-smooth,this paper uses the aggregation function and then gives the smoothing approximation problem of the CVaR model.Thirdly,because the smoothing approximation problel contains the calculation of mathematical expectation,and the mathematical expectation is not easy to obtain under normal circumstances.Therefore,this paper applies the Sample Average Approximation(SAA)method to give the smoothing sample average approximation problem.Finally,this paper gives the convergence results of the global optimal solution of the approximate problem mentioned above in theory.In the fourth chapter,we summarize the main work of this paper,and put forward further consideration of the research on SSCCP.