Intersection Cuts for Bilevel Optimization

The exact solution of bilevel optimization problems is a very challenging task that received more and more attention in recent years, as witnessed by the flourishing recent literature on this topic. In this paper we present ideas and algorithms to solve to proven optimality generic Mixed-Integer Bil...

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Bibliographic Details
Published inInteger Programming and Combinatorial Optimization Vol. 9682; pp. 77 - 88
Main Authors Fischetti, Matteo, Ljubić, Ivana, Monaci, Michele, Sinnl, Markus
Format Book Chapter
LanguageEnglish
Published Switzerland Springer International Publishing AG 01.01.2016
Springer International Publishing
SeriesLecture Notes in Computer Science
Subjects
Bilevel Optimization Problem
Bilevel Problem
Leader Objective Function
Mathematical theory of computation
MILP Solver
Suitable Normalization Factor
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ISBN9783319334608
3319334603
ISSN0302-9743
1611-3349
DOI10.1007/978-3-319-33461-5_7

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Summary:The exact solution of bilevel optimization problems is a very challenging task that received more and more attention in recent years, as witnessed by the flourishing recent literature on this topic. In this paper we present ideas and algorithms to solve to proven optimality generic Mixed-Integer Bilevel Linear Programs (MIBLP’s) where all constraints are linear, and some/all variables are required to take integer values. In doing so, we look for a general-purpose approach applicable to any MIBLP (under mild conditions), rather than ad-hoc methods for specific cases. Our approach concentrates on minimal additions required to convert an effective branch-and-cut MILP exact code into a valid MIBLP solver, thus inheriting the wide arsenal of MILP tools (cuts, branching rules, heuristics) available in modern solvers.
ISBN:9783319334608
3319334603
ISSN:0302-9743
1611-3349
DOI:10.1007/978-3-319-33461-5_7