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- W4298066888 abstract "In this paper, we investigate an optimal control problem with terminal stochastic linear complementarity constraints (SLCC), and its discrete approximation using the relaxation, the sample average approximation (SAA) and the implicit Euler time-stepping scheme. We show the existence of feasible solutions and optimal solutions to the optimal control problem and its discrete approximation under the conditions that the expectation of the stochastic matrix in the SLCC is a Z-matrix or an adequate matrix. Moreover, we prove that the solution sequence generated by the discrete approximation converges to a solution of the original optimal control problem with probability 1 as $epsilon downarrow 0$, $nuto infty $ and $hdownarrow 0$, where $epsilon$ is the relaxation parameter, $nu$ is the sample size and $h$ is the mesh size. We also provide asymptotics of the SAA optimal value and error bounds of the time-stepping method. A numerical example is used to illustrate the existence of optimal solutions, the discretization scheme and error estimation." @default.
- W4298066888 created "2022-10-01" @default.
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- W4298066888 date "2022-08-15" @default.
- W4298066888 modified "2023-10-16" @default.
- W4298066888 title "An Optimal Control Problem with Terminal Stochastic Linear Complementarity Constraints" @default.
- W4298066888 doi "https://doi.org/10.48550/arxiv.2208.07516" @default.
- W4298066888 hasPublicationYear "2022" @default.
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