E. Aiyoshi and K. Shimizu, A solution method for the static constrained stackelberg problem via penalty method. Automatic Control, IEEE Transactions on, vol.29, issue.12, pp.1111-1114, 1984.

?. Akgün, Ç. Barbaros, . Tansel, and . Wood, The multi-terminal maximum-flow network-interdiction problem, European Journal of Operational Research, vol.211, issue.2, pp.241-251, 2011.
DOI : 10.1016/j.ejor.2010.12.011

A. Faiz, R. Al-khayyal, . Horst, M. Panos, and . Pardalos, Global optimization of concave functions subject to quadratic constraints : an application in nonlinear bilevel programming, Annals of Operations Research, vol.34, issue.1, pp.125-147, 1992.

E. Robert, . Aldred, D. Michael, and . Plummer, On matching extensions with prescribed and proscribed edge sets ii. Discrete mathematics, pp.29-40, 1999.

C. Audet, G. Savard, and W. Zghal, New Branch-and-Cut Algorithm for Bilevel Linear Programming, Journal of Optimization Theory and Applications, vol.85, issue.2, pp.353-370, 2007.
DOI : 10.1007/s10957-007-9263-4

O. Michael, . Ball, L. Bruce, . Golden, V. Rakesh et al., Finding the most vital arcs in a network, Operations Research Letters, vol.8, issue.2, pp.73-76, 1989.

A. Bar-noy, S. Khuller, and B. Schieber, The complexity of finding most vital arcs and nodes, 1998.

F. Jonathan and . Bard, An investigation of the linear three level programming problem, Systems, Man and Cybernetics IEEE Transactions on, issue.5, pp.711-717, 1984.

F. Jonathan, . Bard, T. James, and . Moore, A branch and bound algorithm for the bilevel programming problem, SIAM Journal on Scientific and Statistical Computing, vol.11, issue.2, pp.281-292, 1990.

F. Jonathan, . Bard, T. James, and . Moore, An algorithm for the discrete bilevel programming problem, Naval Research Logistics (NRL), vol.39, issue.3, pp.419-435, 1992.

C. Bazgan, S. Toubaline, and Z. Tuza, Complexity of Most Vital Nodes for Independent Set in Graphs Related to Tree Structures, Lecture Notes in Computer Science, vol.17, issue.2, pp.154-166, 2010.
DOI : 10.1016/0895-7177(93)90236-R

C. Bazgan, C. Bentz, C. Picouleau, and B. Ries, Blockers for the Stability Number and the Chromatic Number, Graphs and Combinatorics, vol.309, issue.13, pp.73-90, 2015.
DOI : 10.1007/s00373-013-1380-2
URL : https://hal.archives-ouvertes.fr/hal-01126259

C. Bazgan, S. Toubaline, and Z. Tuza, The most vital nodes with respect to independent set and vertex cover, Discrete Applied Mathematics, vol.159, issue.17, pp.1933-1946, 2011.
DOI : 10.1016/j.dam.2011.06.023

C. Bazgan, S. Toubaline, and D. Vanderpooten, Complexity of determining the most vital elements for the p-median and p-center location problems, Journal of Combinatorial Optimization, vol.309, issue.13, pp.191-207, 2013.
DOI : 10.1007/s10878-012-9469-8
URL : https://hal.archives-ouvertes.fr/hal-01499692

B. Colson, P. Marcotte, and G. Savard, Bilevel programming: A survey, 4OR, vol.3, issue.2, pp.87-107, 2005.
DOI : 10.1007/s10288-005-0071-0

O. Ben-ayed, E. Charles, and . Blair, Computational Difficulties of Bilevel Linear Programming, Operations Research, vol.38, issue.3, pp.556-560, 1990.
DOI : 10.1287/opre.38.3.556

C. Bentz, M. Costa, C. Picouleau, B. Ries, and D. D. Werra, d-Transversals of stable sets and vertex covers in weighted bipartite graphs, Journal of Discrete Algorithms, vol.17, pp.95-102, 2012.
DOI : 10.1016/j.jda.2012.06.002
URL : https://hal.archives-ouvertes.fr/hal-00969156

F. Wayne, . Bialas, H. Mark, and . Karwan, Two-level linear programming, Management science, vol.30, issue.8, pp.1004-1020, 1984.

P. L. Bodic, Variantes non standards de problèmes d'optimisation combinatoire, 2012.

E. Boros, C. Martin, . Golumbic, E. Vadim, and . Levit, On the number of vertices belonging to all maximum stable sets of a graph, Discrete Applied Mathematics, vol.124, issue.1-3, pp.17-25, 2002.
DOI : 10.1016/S0166-218X(01)00327-4

L. Brotcorne, S. Hanafi, and R. Mansi, One-level reformulation of the bilevel knapsack problem using dynamic programming. Discrete Optimization, pp.1-10, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00759250

L. Brotcorne, M. Labbé, P. Marcotte, and G. Savard, A Bilevel Model for Toll Optimization on a Multicommodity Transportation Network, Transportation Science, vol.35, issue.4, pp.345-358, 2001.
DOI : 10.1287/trsc.35.4.345.10433
URL : https://hal.archives-ouvertes.fr/hal-01255608

L. Brotcorne, P. Marcotte, and G. Savard, Bilevel programming : The montreal school. INFOR : Information Systems and Operational Research, pp.231-246, 2008.
DOI : 10.3138/infor.46.4.231
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.461.4381

G. Gerald, . Brown, . Matthew-carlyle, C. Robert, . Harney et al., Interdicting a nuclear-weapons project, Operations Research, vol.57, issue.4, pp.866-877, 2009.

M. Campelo, S. Dantas, and S. Scheimberg, A note on a penalty function approach for solving bilevel linear programs, Journal of Global Optimization, vol.16, issue.3, pp.245-255, 2000.
DOI : 10.1023/A:1008308218364

W. Candler and R. Townsley, A linear two-level programming problem, Computers & Operations Research, vol.9, issue.1, pp.59-76, 1982.
DOI : 10.1016/0305-0548(82)90006-5

M. Sebastian, W. Cioab?, and . Li, The extendability of matchings in strongly regular graphs. the electronic journal of combinatorics, pp.2-34, 2014.

B. Colson, P. Marcotte, and G. Savard, A Trust-Region Method for Nonlinear Bilevel Programming: Algorithm and Computational Experience, Computational Optimization and Applications, vol.42, issue.3, pp.211-227, 2005.
DOI : 10.1007/s10589-005-4612-4

B. Colson, P. Marcotte, and G. Savard, An overview of bilevel optimization, Annals of Operations Research, vol.89, issue.1, pp.235-256, 2007.
DOI : 10.1007/s10479-007-0176-2
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.70.5954

R. Andrew, . Conn, I. Nicholas, . Gould, L. Ph et al., Trust region methods, Siam, vol.1, 2000.

M. Costa, D. De-werra, C. Picouleau, B. Ries, and C. Bentz, Progress in Combinatorial Optimization, chapter Weighted Transversals and Blockers for Some Optimization Problems in Graphs, pp.203-222, 2011.

M. Costa, C. Picouleau, and D. De-werra, Minimum d-blockers and d-transversals in graphs, Journal of Combinatorial Optimization, vol.15, issue.13, pp.857-872, 2011.
DOI : 10.1007/s10878-010-9334-6
URL : https://hal.archives-ouvertes.fr/hal-00973849

M. Costa, C. Picouleau, and D. De-werra, Minimal graphs for matching extensions, Discrete Applied Mathematics, 2015.
DOI : 10.1016/j.dam.2015.11.007
URL : https://hal.archives-ouvertes.fr/hal-01413150

J. Côté, P. Marcotte, and G. Savard, A bilevel modelling approach to pricing and fare optimisation in the airline industry, Journal of Revenue and Pricing Management, vol.2, issue.1, pp.23-36, 2003.
DOI : 10.1057/palgrave.rpm.5170046

S. Dempe, Foundations of bilevel programming, 2002.
DOI : 10.1007/0-387-25570-2_6

S. Dempe, F. Jonathan, and . Bard, Bundle Trust-Region Algorithm for Bilinear Bilevel Programming, Journal of Optimization Theory and Applications, vol.15, issue.2, pp.265-288, 2001.
DOI : 10.1023/A:1017571111854

S. Dempe, V. Kalashnikov, A. Gerardo, N. Pérez-valdés, and . Kalashnykova, Bilevel programming problems, 2015.
DOI : 10.1007/978-3-662-45827-3

S. Denegre, Interdiction and discrete bilevel linear programming, 2011.

S. Denegre, K. Ted, and . Ralphs, A Branch-and-cut Algorithm for Integer Bilevel Linear Programs, pp.65-78, 2009.
DOI : 10.1007/978-0-387-88843-9_4

J. Edmonds, Paths, trees, and flowers, Journal canadien de math??matiques, vol.17, issue.0, pp.449-467, 1965.
DOI : 10.4153/CJM-1965-045-4

E. Erkut, C. Revelle, and Y. Ülküsal, Integer-friendly formulations for the r-separation problem, European Journal of Operational Research, vol.92, issue.2, pp.342-351, 1996.
DOI : 10.1016/0377-2217(94)00348-3

R. Faure, B. Lemaire, and C. Picouleau, Précis de recherche opérationnelle-7e éd. : Méthodes et exercices d'application, 2014.

J. Fortuny-amat and B. Mccarl, A representation and economic interpretation of a two-level programming problem, Journal of the operational Research Society, pp.783-792, 1981.

N. Greg, R. Frederickson, D. Solis-oba, . Fulkerson, C. Gary et al., Increasing the weight of minimum spanning trees Maximizing the minimum source-sink path subject to a budget constraint, Mathematical Programming, pp.244-266116, 1977.

R. Michael, . Garey, S. David, and . Johnson, Computers and intractability : a guide to NP-completeness, 1979.

B. Golden, A problem in network interdiction, Naval Research Logistics Quarterly, vol.23, issue.4, pp.711-713, 1978.
DOI : 10.1002/nav.3800250412

J. Han, J. Lu, Y. Hu, and G. Zhang, Tri-level decision-making with multiple followers: Model, algorithm and case study, Information Sciences, vol.311, pp.182-204, 2015.
DOI : 10.1016/j.ins.2015.03.043

P. Hansen, B. Jaumard, and G. Savard, New Branch-and-Bound Rules for Linear Bilevel Programming, SIAM Journal on Scientific and Statistical Computing, vol.13, issue.5, pp.1194-1217, 1992.
DOI : 10.1137/0913069

W. Donald, . Hearn, V. Motakuri, and . Ramana, Solving congestion toll pricing models, 1998.

Y. Ishizuka and E. Aiyoshi, Double penalty method for bilevel optimization problems, Annals of Operations Research, vol.21, issue.1, pp.73-88, 1992.
DOI : 10.1007/BF02098173

E. Israeli and R. Wood, Shortest-path network interdiction, Networks, vol.17, issue.2, pp.97-111, 2002.
DOI : 10.1002/net.10039
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.104.7027

B. Jaumard, J. Savard, and . Xiong, An exact algorithm for convex quadratic bilevel programming. Draft paper, 2000.

G. Robert and . Jeroslow, The polynomial hierarchy and a simple model for competitive analysis, Mathematical programming, vol.32, issue.2, pp.146-164, 1985.

Y. Bahar, V. Kara, and . Verter, Designing a road network for hazardous materials transportation, Transportation Science, vol.38, issue.2, pp.188-196, 2004.

L. Khachiyan, E. Boros, K. Borys, K. Elbassioni, V. Gurvich et al., On Short Paths Interdiction Problems: Total and Node-Wise Limited Interdiction, Theory of Computing Systems, pp.204-233, 2008.
DOI : 10.1007/s00224-007-9025-6
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.398.4639

M. Köppe, M. Queyranne, C. T. , and R. , Parametric Integer Programming Algorithm for Bilevel Mixed Integer Programs, Journal of Optimization Theory and Applications, vol.16, issue.1, pp.137-150, 2010.
DOI : 10.1007/s10957-010-9668-3

M. Labbé, P. Marcotte, and G. Savard, A Bilevel Model of Taxation and Its Application to Optimal Highway Pricing, Management Science, vol.44, issue.12-part-1, pp.1608-1622, 1998.
DOI : 10.1287/mnsc.44.12.1608

C. Lee, Variations of maximum-clique transversal sets on graphs, Annals of Operations Research, vol.189, issue.1, pp.21-66, 2010.
DOI : 10.1007/s10479-009-0673-6

W. Hendrik and . Jr, Integer programming with a fixed number of variables, Mathematics of operations research, vol.8, issue.4, pp.538-548, 1983.

K. Levenberg, A method for the solution of certain non-linear problems in least squares, Quarterly of Applied Mathematics, vol.2, issue.2, 1944.
DOI : 10.1090/qam/10666

G. Liu, J. Han, and S. Wang, A trust region algorithm for bilevel programing problems, Chinese Science Bulletin, vol.75, issue.10, pp.820-824, 1998.
DOI : 10.1007/BF03182744

P. Loridan and J. Morgan, Weak via strong Stackelberg problem: New results, Journal of Global Optimization, vol.13, issue.n.1, pp.263-287, 1996.
DOI : 10.1007/BF00121269

V. Foad-mahdavi-pajouh, E. L. Boginski, and . Pasiliao, Minimum vertex blocker clique problem, Networks, vol.309, issue.1, pp.48-64, 2014.
DOI : 10.1002/net.21556

P. Marcotte, Network design problem with congestion effects: A case of bilevel programming, Mathematical Programming, pp.142-162, 1986.
DOI : 10.1007/BF01580580

T. James, . Moore, F. Jonathan, and . Bard, The mixed integer linear bilevel programming problem, Operations research, vol.38, issue.5, pp.911-921, 1990.

D. Michael and . Plummer, Extending matchings in graphs : a survey, Discrete Mathematics, vol.127, issue.1, pp.277-292, 1994.

B. Ries, C. Bentz, C. Picouleau, D. De-werra, M. Costa et al., Blockers and transversals in some subclasses of bipartite graphs : When caterpillars are dancing on a grid Solving the bi-objective maximum-flow network-interdiction problem, Discrete Mathematics INFORMS Journal on Computing, vol.31069, issue.192, pp.132-146175, 2007.

G. Savard and J. Gauvin, The steepest descent direction for the nonlinear bilevel programming problem, Operations Research Letters, vol.15, issue.5, pp.265-272, 1994.
DOI : 10.1016/0167-6377(94)90086-8

A. Schrijver, Combinatorial optimization : polyhedra and efficiency, 2003.

S. Dempe, Bilevel Programming, Dekan der Fak. für Mathematik und Informatik, 2003.
DOI : 10.1007/0-387-25570-2_6

A. G. Mershaand and S. Dempe, Linear bilevel programming with upper level constraints depending on the lower level solution, Applied Mathematics and Computation, vol.180, issue.1, pp.247-254, 2006.
DOI : 10.1016/j.amc.2005.11.134

K. Shimizu and E. Aiyoshi, A new computational method for Stackelberg and min-max problems by use of a penalty method, IEEE Transactions on Automatic Control, vol.26, issue.2, pp.460-466, 1981.
DOI : 10.1109/TAC.1981.1102607

L. Vicente, G. Savard, and J. Judice, Discrete linear bilevel programming problem, Journal of Optimization Theory and Applications, vol.81, issue.3, pp.597-614, 1996.
DOI : 10.1007/BF02275351

L. Vicente, G. Savard, and J. Júdice, Descent approaches for quadratic bilevel programming, Journal of Optimization Theory and Applications, vol.7, issue.2, pp.379-399, 1994.
DOI : 10.1007/BF02191670

D. White, Penalty Function Approach to Linear Trilevel Programming, Journal of Optimization Theory and Applications, vol.11, issue.1, pp.183-197, 1997.
DOI : 10.1023/A:1022610103712

J. Douglas, G. White, and . Anandalingam, A penalty function approach for solving bi-level linear programs, Journal of Global Optimization, vol.3, issue.4, pp.397-419, 1993.

R. Wollmer, Removing Arcs from a Network, Operations Research, vol.12, issue.6, pp.934-940, 1964.
DOI : 10.1287/opre.12.6.934
URL : http://www.dtic.mil/get-tr-doc/pdf?AD=AD0601643

R. Kevin and W. , Deterministic network interdiction, Mathematical and Computer Modelling, vol.17, issue.2, pp.1-18, 1993.

R. Zenklusen, B. Ries, C. Picouleau, D. D. Werra, M. Costa et al., Blockers and transversals, Discrete Mathematics, vol.309, issue.13, pp.4306-4314, 2009.
DOI : 10.1016/j.disc.2009.01.006
URL : https://hal.archives-ouvertes.fr/hal-00975349