A Penalty Method for Linear Bilevel Programming Problems

Amouzegar, Mahyar A.; Moshirvaziri, Khosrow

doi:10.1007/978-1-4613-0307-7_11

Cited by 14 publications

(8 citation statements)

References 19 publications

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“…Actually, it can be shown that LBP and P(M) are both infeasible or unbounded for all M ≥ 0 or else there is a correspondence between the global optimal solutions of the problems for all M ≥ M 0 , for some finite value M 0 ≥ 0 (Campêlo and Scheimberg, 2001). This equivalence has supported some methods for finding global optimal solutions of LBP (see, for example, Bard (1984), White and Anandalingam (1993), Amouzegar and Moshirvaziri (1998) and Campêlo and Scheimberg (2001)). …”

Section: Preliminariesmentioning

confidence: 91%

“…This formulation has been extensively studied in the literature. Basic properties and solution methods are presented by Bialas and Karwan (1984), Hansen, Jaumard, and Savard (1992), Júdice and Faustino (1992), White and Anandalingam (1993), Amouzegar and Moshirvaziri (1998) and Campêlo and Scheimberg (2001), for instance. Also, we refer to Luo et al (1996) for an approach in the framework of mathematical programs with equilibrium constraints (MPEC).…”

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confidence: 99%

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A Simplex Approach for Finding Local Solutions of a Linear Bilevel Program by Equilibrium Points

Campêlo

Scheimberg

2005

Ann Oper Res

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In this paper, a linear bilevel programming problem (LBP) is considered. Local optimality conditions are derived. They are based on the notion of equilibrium point of an exact penalization for LBP. It is described how an equilibrium point can be obtained with the simplex method. It is shown that the information in the simplex tableaux can be used to get necessary and sufficient local optimality conditions for LBP. Based on these conditions, a simplex type algorithm is proposed, which attains a local solution of LBP by moving in equilibrium points. A numerical example illustrates how the algorithm works. Some computational results are reported.

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Section: Preliminariesmentioning

confidence: 91%

mentioning

confidence: 99%

A Simplex Approach for Finding Local Solutions of a Linear Bilevel Program by Equilibrium Points

Campêlo

Scheimberg

2005

Ann Oper Res

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“…This is shown in the papers [16,50,436], as well as [437]. A penalty function method for linear bilevel problems can be found in [8]. 338 S. DEMPE…”

Section: Solution Algorithmsmentioning

confidence: 96%

Annotated Bibliography on Bilevel Programming and Mathematical Programs with Equilibrium Constraints

2003

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“…Duality theory has been used previously to construct exact penalty functions for linear and quadratic bi-level problems, see e.g. [2,52,89,90]. In these methods, the duality gap of the lower-level problem is included in the upper-level objective function to determine an optimal upper-level solution that simultaneously optimizes the lower-level objective.…”

Section: Computational Complexitymentioning

confidence: 99%

“…2 We used the standard settings of BARON, with the exception that we changed the optimality tolerance to 10 −5 .…”

Section: Computational Studymentioning

confidence: 99%

Pessimistic Bilevel Optimization

Wiesemann¹,

Tsoukalas²,

Kleniati³

et al. 2013

SIAM J. Optim.

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We study a variant of the pessimistic bi-level optimization problem, which comprises constraints that must be satisfied for any optimal solution of a subordinate (lower-level) optimization problem. We present conditions that guarantee the existence of optimal solutions in such a problem, and we characterize the computational complexity of various subclasses of the problem. We then focus on problem instances that may lack convexity, but that satisfy a certain independence property. We develop convergent approximations for these instances, and we derive an iterative solution scheme that is reminiscent of the discretization techniques used in semi-infinite programming. We also present a computational study that illustrates the numerical behavior of our algorithm on standard benchmark instances.

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A Penalty Method for Linear Bilevel Programming Problems

Cited by 14 publications

References 19 publications

A Simplex Approach for Finding Local Solutions of a Linear Bilevel Program by Equilibrium Points

A Simplex Approach for Finding Local Solutions of a Linear Bilevel Program by Equilibrium Points

Annotated Bibliography on Bilevel Programming and Mathematical Programs with Equilibrium Constraints

Pessimistic Bilevel Optimization

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