Pessimistic Bilevel Linear Optimization

Authors

  • S. Dempe TU Bergakademie Freiberg, Germany
  • G. Luo Guangdong University of Finance, China
  • S. Franke TU Bergakademie Freiberg, Germany

DOI:

https://doi.org/10.3126/jnms.v1i1.42165

Keywords:

Pessimistic bilevel optimization, Bilevel linear optimization problem, Nonconvex optimization, Basic matrix, Optimal value function, Minimax problem, Local and global optimization, Solution algorithms, Enumeration algorithm, Descent algorithm

Abstract

In this paper, we investigate the pessimistic bilevel linear optimization problem (PBLOP). Based on the lower level optimal value function and duality, the PBLOP can be transformed to a single-level while nonconvex and nonsmooth optimization problem. By use of linear optimization duality, we obtain a tractable and equivalent transformation and propose algorithms for computing global or local optimal solutions. One small example is presented to illustrate the feasibility of the method.  

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Author Biographies

S. Dempe, TU Bergakademie Freiberg, Germany

Institute of Numerical Mathematics and Optimization

G. Luo, Guangdong University of Finance, China

Department of Applied Mathematics

S. Franke, TU Bergakademie Freiberg, Germany

Institute of Numerical Mathematics and Optimization

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Published

2018-02-11

How to Cite

Dempe, S., Luo, G., & Franke, S. (2018). Pessimistic Bilevel Linear Optimization. Journal of Nepal Mathematical Society, 1(1), 1–10. https://doi.org/10.3126/jnms.v1i1.42165

Issue

Vol. 1 No. 1 (2018)

Section

Articles

License

© Nepal Mathematical Society