Numerical Methods For The Second-order Cone Constrained Stochastic Variational Inequality Problems

Variational inequality problem is a branch of mathematical programming problem.Since1960s,it has been widely studied by scholars and subsequently applied in physics,traffic,economy,engineering and many other fields.However,there are many uncertainties such as climate,policy and temperature in practical problems,which need stochastic models to solve,such as stochastic linear complementarity problem,stochastic complementarity problem,stochastic variational inequality problem,etc.In this paper,we study the second-order cone constrained stochastic variational inequality?SOCCSVI?problems.The sample average approximation?SAA?method combined with SOC-complementarity functions is uesd to solve the problems.Firstly,the SAA method is used to transform the SOCCSVI problem into a SAA problem.In chapter 3,by combining the SOC-complementarity functions?_FB and?_FBrespectively,the SAA problem is transformed into a equation problem and the nonsingularity of the equation operation's Jacobian matrix is proved.The modified Newton algorithm is constructed to solve the equation problem.We give three numerical experiments and analyze the results to show the effectiveness of the proposed method.In chapter 4,the SAA problem is transformed into a equation problem by combining the SOC-complementarity functions?_FB-pand?_NR-prespectively,and the nonsingularity of the equation operation's Jacobian matrix is proved.Using the modified Newton algorithm to solve the equation problem,we give three numerical experiments to show that the SAA method combined with SOC-complementarity functions?_FB-pand?_NR-pcan effectively solve SOCCSVI problems.Finally,according to the experiments results,we analyz the effects of these four SOC-complementarity functions in solving the SOCCSVI problems.