2014
DOI: 10.2298/fil1408619z
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A global solution method for semivectorial bilevel programming problem

Abstract: In this paper, we consider a class of semivectorial bilevel programming problem. An exact penalty function is proposed for such a problem. Based on this penalty function, an algorithm, which can obtain a global solution of the original problem, is presented. Finally, some numerical results illustrate its feasibility.

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Cited by 5 publications
(2 citation statements)
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References 17 publications
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“…Considering weakly efficient solutions to the lower level problem, Bonnel and Morgan (Bonnel and Morgan, 2006) proposed a solution approach based on a penalty function. Ankhili and Mansouri (Ankhili and Mansouri, 2009), Zheng and Wan (Zheng and Wan, 2011), Zheng et al (Zheng, Chen and Cao, 2014), and Ren and Wang (Ren and Wang, 2016) developed penalty function methods to compute the optimistic solution to the SVBP with a multi-objective linear programming (MOLP) problem at the lower level. Calvete and Galé (Calvete and Galé, 2011) also focused on bilevel problems with a MOLP lower level problem (with all constraints linear and the upper level objective function quasiconcave).…”
Section: 2mentioning
confidence: 99%
“…Considering weakly efficient solutions to the lower level problem, Bonnel and Morgan (Bonnel and Morgan, 2006) proposed a solution approach based on a penalty function. Ankhili and Mansouri (Ankhili and Mansouri, 2009), Zheng and Wan (Zheng and Wan, 2011), Zheng et al (Zheng, Chen and Cao, 2014), and Ren and Wang (Ren and Wang, 2016) developed penalty function methods to compute the optimistic solution to the SVBP with a multi-objective linear programming (MOLP) problem at the lower level. Calvete and Galé (Calvete and Galé, 2011) also focused on bilevel problems with a MOLP lower level problem (with all constraints linear and the upper level objective function quasiconcave).…”
Section: 2mentioning
confidence: 99%
“…The optimistic formulation assumes that the follower accepts any efficient solution to the lower level problem. Other methods based on penalty functions were further proposed by Ankhili and Mansouri [23], Zheng and Wan [24], Zheng et al [25] and Ren and Wang [26] for the SVBP with multi-objective linear programming (MOLP) problems in the lower level. Calvete and Galé [27] also focused on bilevel problems with lower level MOLP problems.…”
Section: Semivectorial Bilevel Programmingmentioning
confidence: 99%