Bilevel Programming

Dempe, Stephan

doi:10.1007/0-387-25570-2_6

Cited by 282 publications

(473 citation statements)

References 36 publications

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“…The BLPP has been a subject of intense research and several notable volumes have been published to date [7,32,72,87]. At the same time applications of BLPP can be found in fields as diverse as chemical engineering [49], robot motion planning and control [72], production planning [8] occurring in a multitude of disciplines [7].…”

Section: Fig 1 Pictoral Representation Of a Blppmentioning

confidence: 99%

“…At the same time applications of BLPP can be found in fields as diverse as chemical engineering [49], robot motion planning and control [72], production planning [8] occurring in a multitude of disciplines [7]. In tandem, there has been much work on the development of solution methodologies (see [26,32] for a review of these).…”

Section: Fig 1 Pictoral Representation Of a Blppmentioning

confidence: 99%

“…Unfortunately a counterexample in [67] demonstrates that PIPA can converge to a nonstationary point. Subsequent research has led to the development of many other techniques to solve the MPEC such as the piecewise sequential quadratic programming in [72], branch-and-bound [6], nonsmooth approaches [32,87] and smoothing methods [38].…”

Section: Solution Algorithms For the Blppmentioning

confidence: 99%

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A Metaheuristic Framework for Bi-level Programming Problems with Multi-disciplinary Applications

Koh

2013

Metaheuristics for Bi-Level Optimization

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Bi-level programming problems arise in situations when the decision maker has to take into account the responses of the users to his decisions. Several problems arising in engineering and economics can be cast within the bi-level programming framework. The bi-level programming model is also known as a Stackleberg or leader-follower game in which the leader chooses his variables so as to optimise his objective function, taking into account the response of the follower(s) who separately optimise their own objectives, treating the leader's decisions as exogenous. In this chapter, we present a unified framework fully consistent with the Stackleberg paradigm of bi-level programming that allows for the integration of meta-heuristic algorithms with traditional gradient based optimisation algorithms for the solution of bi-level programming problems. In particular we employ Differential Evolution as the main meta-heuristic in our proposal. We subsequently apply the proposed method (DEBLP) to a range of problems from many fields such as transportation systems management, parameter estimation and game theory. It is demonstrated that DEBLP is a robust and powerful search heuristic for this class of problems characterised by non smoothness and non convexity.

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Section: Fig 1 Pictoral Representation Of a Blppmentioning

confidence: 99%

Section: Fig 1 Pictoral Representation Of a Blppmentioning

confidence: 99%

Section: Solution Algorithms For the Blppmentioning

confidence: 99%

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A Metaheuristic Framework for Bi-level Programming Problems with Multi-disciplinary Applications

Koh

2013

Metaheuristics for Bi-Level Optimization

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“…Incidentally observe that our assumption on the weights w corresponds to what is known as the pessimistic paradigm [7]. In fact, among all possible solutions to (6) with the same F value, we choose the one with the maximum number of defaulting agents.…”

Section: Return Tomentioning

confidence: 99%

Computing Optimal Recovery Policies for Financial Markets

Benth

Dahl

Mannino

2012

Operations Research

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The current nancial crisis motivates the study of correlated defaults in nancial systems. In this paper we focus on such a model which is based on Markov random elds. This is a probabilistic model where uncertainty in default probabilities incorporates expert's opinions on the default risk (based on various credit ratings). We consider a bilevel optimization model for nding an optimal recovery policy: which companies should be supported given a xed budget. This is closely linked to the problem of nding a maximum likelihood estimator of the defaulting set of agents, and we show how to compute this solution e ciently using combinatorial methods. We also prove properties of such optimal solutions. A practical procedure for estimation of model parameters is also given. Computational examples are presented and experiments indicate that our methods can nd optimal recovery policies for up to about 100 companies. The overall approach is evaluated on a real-world problem concerning the major banks in Scandinavia and public loans. To our knowledge this is a rst attempt to apply combinatorial optimization techniques to this important, and expanding, area of default risk analysis.

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“…There are several frameworks of bilevel programs and a number of approaches to their study and applications; see the book [11] and the extended introduction to [12] for more discussions and references. The so-called optimistic version in bilevel programming reads as follows:…”

Section: Bilevel Programmingmentioning

confidence: 99%

New Applications of Variational Analysis to Optimization and Control

Mordukhovich

2009

IFIP Advances in Information and Communication Technology

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Abstract. We discuss new applications of advanced tools of variational analysis and generalized differentiation to a number of important problems in optimization theory, equilibria, optimal control, and feedback control design. The presented results are largely based on the recent work by the author and his collaborators. Among the main topics considered and briefly surveyed in this paper are new calculus rules for generalized differentiation of nonsmooth and set-valued mappings; necessary and sufficient conditions for new notions of linear subextremality and suboptimality in constrained problems; optimality conditions for mathematical problems with equilibrium constraints; necessary optimality conditions for optimistic bilevel programming with smooth and nonsmooth data; existence theorems and optimality conditions for various notions of Pareto-type optimality in problems of multiobjective optimization with vector-valued and set-valued cost mappings; Lipschitzian stability and metric regularity aspects for constrained and variational systems.

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Bilevel Programming

Cited by 282 publications

References 36 publications

A Metaheuristic Framework for Bi-level Programming Problems with Multi-disciplinary Applications

A Metaheuristic Framework for Bi-level Programming Problems with Multi-disciplinary Applications

Computing Optimal Recovery Policies for Financial Markets

New Applications of Variational Analysis to Optimization and Control

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