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Operations Research Transactions >

2015 , Vol. 19 >Issue 2: 29 - 36

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2015.02.003

A global optimization method for solving the linear semivectorial bilevel programming problem

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  • 1. School of Information and Mathematics, Yangtze University, Jingzhou 434023, Hubei, China; 2. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

Received date: 2014-08-29

  Online published: 2015-06-15

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Abstract

In this paper, we are concerned with global optimization approach for solving the linear semivectorial bilevel programming (LSBP) problem. Using the duality gap of the lower level programs, we construct the corresponding penalized problem. By analyzing the relationships between the optimal solutions of the original problem and the vertices of the feasible region of the penalized problem, we transform the LSBP problem to a series of linear programming problems. Then, the global optimal solution of the LSBP problem can be obtained by solving a series of linear programming problems. The numerical results show that the algorithm proposed is feasible to the LSBP problem.

Key words： semivectorial bilevel programming; duality; penalty function; global optimization solution

Cite this article

LV Yibing, WAN Zhongping . A global optimization method for solving the linear semivectorial bilevel programming problem[J]. Operations Research Transactions, 2015 , 19(2) : 29 -36 . DOI: 10.15960/j.cnki.issn.1007-6093.2015.02.003

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