Two-stage stochastic variational inequalities: an ERM-solution procedure |
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Authors: | Xiaojun Chen Ting Kei Pong Roger J-B Wets |
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Institution: | 1.Department of Applied Mathematics,The Hong Kong Polytechnic University,Kowloon,Hong Kong;2.Department of Mathematics,University of California, Davis,Davis,USA |
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Abstract: | We propose a two-stage stochastic variational inequality model to deal with random variables in variational inequalities, and formulate this model as a two-stage stochastic programming with recourse by using an expected residual minimization solution procedure. The solvability, differentiability and convexity of the two-stage stochastic programming and the convergence of its sample average approximation are established. Examples of this model are given, including the optimality conditions for stochastic programs, a Walras equilibrium problem and Wardrop flow equilibrium. We also formulate stochastic traffic assignments on arcs flow as a two-stage stochastic variational inequality based on Wardrop flow equilibrium and present numerical results of the Douglas–Rachford splitting method for the corresponding two-stage stochastic programming with recourse. |
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