A discretization iteration approach for solving a class of semivectorial bilevel programming problem

Volume 9, Issue 5, pp 2888--2899 http://dx.doi.org/10.22436/jnsa.009.05.83

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Authors

Yibing Lv - School of Information and Mathematics, Yangtze University, Jingzhou 434023, P. R. China. Jiawei Chen - School of Mathematics and Statistics, Southwest University, Chongqing 400715, P. R. China.

Abstract

The pessimistic optimal solution of the semivectorial bilevel programming problem with no upper level variables in the lower level constraints is concerned. Based on the scalarization techniques and optimal value transforming approach for the lower level problem, the semivectorial bilevel programming problem is transformed into the corresponding infinite-dimensional optimization problem. Then, a discretization iterative algorithm is proposed, and the convergence of the algorithm is also analyzed. The numerical results show that the algorithm is feasible for the pessimistic optimal solution of the semivectorial bilevel programming problem studied.

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Keywords

• Semivectorial bilevel programming problem
• optimal value function
• discretization iteration
• pessimistic solution.

MSC

•  90C26
•  90C30.

References

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