2005
DOI: 10.1007/s10288-005-0071-0
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Bilevel programming: A survey

Abstract: This paper provides an introductory survey of a class of optimization problems known as bilevel programming. We motivate this class through a simple application, and then proceed with the general formulation of bilevel programs. We consider various cases (linear, linear-quadratic, nonlinear), describe their main properties and give an overview of solution approaches.

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Cited by 377 publications
(240 citation statements)
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References 86 publications
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“…If the constraint sets are non-convex, then a near optimal solution can be solved by various numerical methods, e.g. (Garcia, et al, 1989;Bemporad and Morari, 1999;Qin and Badgwell, 2003;Colson, et al, 2005).…”
Section: Mpc Concept and Formulation 42mentioning
confidence: 99%
“…If the constraint sets are non-convex, then a near optimal solution can be solved by various numerical methods, e.g. (Garcia, et al, 1989;Bemporad and Morari, 1999;Qin and Badgwell, 2003;Colson, et al, 2005).…”
Section: Mpc Concept and Formulation 42mentioning
confidence: 99%
“…Bilevel problems are notoriously hard to solve, already in the case when both the inner and outer problems are linear programs, which pretty much is the most simple bilevel problem possible [13,4,9]. The case when the inner problem is convex for fixed outer variables is somewhat more manageable than the general case, since the optimality condition on the inner variables can be encoded using KKT conditions.…”
Section: A Bilevel Programming Approach To Recursive Feasibility Analmentioning
confidence: 99%
“…In principle, the complementarity structure allows us to solve the problem using brute-force enumeration and linear programming. In practice, it means that we can use standard mixedinteger reformulations of the problem [9].…”
Section: A Linear Bilevel Alternativementioning
confidence: 99%
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“…References can be found in Vicente and Calamai (1994); Dempe (2002); Colson et al (2005Colson et al ( , 2007. Refer to Labbé and Violin (2013) for more detail on the bilevel programming and price setting problems.…”
Section: Introductionmentioning
confidence: 99%