Robust weighted expected residual minimization formulation for stochastic vector variational inequalities


Authors

Yong Zhao - College of Mathematics and Statistics, Chongqing JiaoTong University, Chongqing 400074, China. Zai Yun Peng - College of Mathematics and Statistics, Chongqing JiaoTong University, Chongqing 400074, China. Yun Bin Zhao - School of Mathematics, University of Birmingham, Birmingham, UK.


Abstract

In order to deal with (stochastic) multi-objective optimization problems, a robust Pareto optimal solution by minimizing the worst case weighted sum of objectives on a given weight set is considered [J. Hu, S. Mehrotra, Oper. Res., \(\textbf{60}\) (2011), 936--953], [J. Hu, T. Homem-de-Mello, S. Mehrotra, Manuscript, (2010)]. Based on this idea, we introduce a new class of deterministic model for stochastic vector variational inequalities, called robust weighted expected residual minimization model. Then we propose sample average approximation (SAA) approach to solve robust weighted expected residual minimization problems. Some convergence results are established for the approximation problem in terms of the optimal value and the set of optimal solutions.


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ISRP Style

Yong Zhao, Zai Yun Peng, Yun Bin Zhao, Robust weighted expected residual minimization formulation for stochastic vector variational inequalities, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 11, 5825--5833

AMA Style

Zhao Yong, Peng Zai Yun, Zhao Yun Bin, Robust weighted expected residual minimization formulation for stochastic vector variational inequalities. J. Nonlinear Sci. Appl. (2017); 10(11):5825--5833

Chicago/Turabian Style

Zhao, Yong, Peng, Zai Yun, Zhao, Yun Bin. "Robust weighted expected residual minimization formulation for stochastic vector variational inequalities." Journal of Nonlinear Sciences and Applications, 10, no. 11 (2017): 5825--5833


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