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Pessimistic Bi-Level Optimisation

Wolfram Wiesemann (wwiesema***at***imperial.ac.uk)
Angelos Tsoukalas (maurostsouk***at***googlemail.com)
Polyxeni-Margarita Kleniati (polyxeni.kleniati03***at***imperial.ac.uk)
Berc Rustem (br***at***imperial.ac.uk)

Abstract: Bi-level problems are optimisation problems in which some of the decision variables must optimise a subordinate (lower-level) problem. In general, the lower-level problem can possess multiple optimal solutions. One therefore distinguishes between optimistic formulations, which assume that the most favourable lower-level solution is implemented, and pessimistic formulations, in which the most adverse lower-level solution is adopted. In this paper we study the pessimistic bi-level problem without making any convexity assumptions. We analyse the structural properties of this problem, and we develop a convergent sequence of solvable approximations. We then propose an iterative solution scheme, and we present a computational study that investigates the numerical behaviour of the algorithm.

Keywords: Global Optimisation; Pessimistic Bi-Level Problem; Computational Complexity

Category 1: Global Optimization (Theory )

Citation: Working Paper, Imperial College London and Massachusetts Institute of Technology, January 2012

Download: [Compressed Postscript][PDF]

Entry Submitted: 01/28/2012
Entry Accepted: 01/28/2012
Entry Last Modified: 07/23/2012

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