On Bilevel Optimization with Inexact Follower

References

• Aboussoror A, Adly S, Saissi FE (2017) Strong-weak nonlinear bilevel problems: existence of solutions in a sequential setting. Set-Valued Variational Anal. 25(1):113–132.Crossref, Google Scholar
• Aboussoror A, Loridan P (1995) Strong-weak stackelberg problems in finite dimensional spaces. Serdica Math. J. 21(2):151–170.Google Scholar
• Aboussoror A, Mansouri A (2005) Weak linear bilevel programming problems: existence of solutions via a penalty method. J. Math. Anal. Appl. 304(1):399–408.Crossref, Google Scholar
• Adams W, Forrester R (2005) A simple recipe for concise mixed 0-1 linearizations. Oper. Res. Lett. 33(1):55–61.Crossref, Google Scholar
• Arroyo JM, Galiana FD (2005) On the solution of the bilevel programming formulation of the terrorist threat problem. IEEE Trans. Power Systems 20(2):789–797.Crossref, Google Scholar
• Audet C, Haddad J, Savard G (2007a) Disjunctive cuts for continuous linear bilevel programming. Optim. Lett. 1(3):259–267.Crossref, Google Scholar
• Audet C, Savard G, Zghal W (2007b) New branch-and-cut algorithm for bilevel linear programming. J. Optim. Theory Appl. 134(2):353–370.Crossref, Google Scholar
• Audet C, Hansen P, Jaumard B, Savard G (1997) Links between linear bilevel and mixed 0-1 programming problems. J. Optim. Theory Appl. 93(2):273–300.Crossref, Google Scholar
• Balas E, Zemel E (1980) An algorithm for large zero-one knapsack problems. Oper. Res. 28(5):1130–1154.Link, Google Scholar
• Bard JF (1998) Practical bilevel optimization: algorithms and applications. Nonconvex optimization and its applications (Kluwer Academic Publishers, Dordrecht, Netherlands).Crossref, Google Scholar
• Bard JF, Plummer J, Sourie JC (2000) A bilevel programming approach to determining tax credits for biofuel production. Eur. J. Oper. Res. 120(1):30–46.Crossref, Google Scholar
• Beheshti B, Özaltın O, Zare MH, Prokopyev OA (2015) Exact solution approach for a class of nonlinear bilevel knapsack problems. J. Global Optim. 61(2):291–310.Crossref, Google Scholar
• Bertsimas D, Sim M (2003) Robust discrete optimization and network flows. Math. Programming 98(1):49–71.Crossref, Google Scholar
• Bertsimas D, Sim M (2004) The price of robustness. Oper. Res. 52(1):35–53.Link, Google Scholar
• Borrero JS, Prokopyev OA, Saure D (2016) Sequential shortest path interdiction with incomplete information. Decision Anal. 13(1):68–98.Link, Google Scholar
• Borrero JS, Prokopyev OA, Saure D (2019) Sequential interdiction with incomplete information and learning. Oper. Res. 67(1):33–57.Link, Google Scholar
• Brotcorne L, Hanafi S, Mansi R (2009) A dynamic programming algorithm for the bilevel knapsack problem. Oper. Res. Lett. 37(3):215–218.Crossref, Google Scholar
• Brown G, Carlyle M, Salmeron J, Wood K (2006) Defending critical infrastructure. Interfaces 36(6):530–544.Link, Google Scholar
• Burgard A, Pharkya P, Maranas C (2003) Optknock: A bilevel programming framework for identifying gene knockout strategies for microbial strain optimization. Biotech. Bioengrg. 84(6):647–657.Crossref, Google Scholar
• Cao D, Leung L (2002) A partial cooperation model for non-unique linear two-level decision problems. Eur. J. Oper. Res. 140(1):134–141.Crossref, Google Scholar
• Caprara A, Carvalho M, Lodi A, Woeginger GJ (2013) A complexity and approximability study of the bilevel knapsack problem. Goemans M, Correa J, eds. Integer Programming and Combinatorial Optimization, Lecture Notes in Computer Science, vol. 7801 (Springer, Berlin, Heidelberg), 98–109.Crossref, Google Scholar
• Caprara A, Carvalho M, Lodi A, Woeginger GJ (2014) A study on the computational complexity of the bilevel knapsack problem. SIAM J. Optim. 24(2):823–838.Crossref, Google Scholar
• Caprara A, Carvalho M, Lodi A, Woeginger GJ (2016) Bilevel knapsack with interdiction constraints. INFORMS J. Comput. 28(2):319–333.Link, Google Scholar
• Caramia M, Mari R (2015) Enhanced exact algorithms for discrete bilevel linear problems. Optim. Lett. 9(7):1447–1468.Crossref, Google Scholar
• Colson B, Marcotte P, Savard G (2007) An overview of bilevel optimization. Ann. Oper. Res. 153(1):235–256.Crossref, Google Scholar
• Côté J-P, Savard G (2003) A bilevel modelling approach to pricing and fare optimization in the airline industry. J. Revenue Pricing Management 2(1):23–26.Crossref, Google Scholar
• CPLEX (2016) http://www-01.ibm.com/software/info/ilog/. Accessed on January 7, 2016.Google Scholar
• Dempe S (2002) Foundations of Bilevel Programming (Kluwer Academic Publishers, Dordrecht, Netherlands).Google Scholar
• Dempe S, Richter K (2000) Bilevel programming with knapsack constraints. Central Eur. J. Oper. Res. 8(2):93–107.Google Scholar
• DeNegre ST, Ralphs TK (2009) A branch-and-cut algorithm for bilevel integer programming. Chinneck JW, Kristjansson B, Saltzman MJ, eds. Proc. 11th INFORMS Comput. Soc. Meeting (Springer, New York), 65–78.Google Scholar
• Deng X (1998) Complexity issues in bilevel linear programming. Pardalos P, Migdalas A, Varbrand P, eds. Multilevel optimization: algorithms and applications (Springer, New York), 149–164.Crossref, Google Scholar
• Fayard D, Plateau G (1982) An algorithm for the solution of the 0–1 knapsack problem. Computing 28(3):269–287.Crossref, Google Scholar
• Fudenberg D, Tirole J (1991) Game Theory (MIT Press, Cambridge, MA).Google Scholar
• Garey M, Johnson D (1979), Computers and Intractability: A Guide to the Theory of NP-Completeness (WH Freeman, San Francisco).Google Scholar
• Gendreau M, Potvin J-Y (2010) Handbook of Metaheuristics, vol. 2 (Springer, New York).Crossref, Google Scholar
• Guan P, He M, Zhuang J, Hora SC (2017) Modeling a multitarget attacker–defender game with budget constraints. Decision Anal. 14(2):87–107.Link, Google Scholar
• Gzara F (2013) A cutting plane approach for bilevel hazardous material transport network design. Oper. Res. Lett. 41(1):40–46.Crossref, Google Scholar
• Harker PT, Pang J-S (1988) Existence of optimal solutions to mathematical programs with equilibrium constraints. Oper. Res. Lett. 7(2):61–64.Crossref, Google Scholar
• Hogarth RM, Karelaia N (2005) Simple models for multiattribute choice with many alternatives: When it does and does not pay to face trade-offs with binary attributes. Management Sci. 51(12):1860–1872.Link, Google Scholar
• Horowitz E, Sahni S (1974) Computing partitions with applications to the knapsack problem. J. ACM 21(2):277–292.Crossref, Google Scholar
• Ibarra OH, Kim CE (1975) Fast approximation algorithms for the knapsack and sum of subset problems. J. ACM 22(4):463–468.Crossref, Google Scholar
• Kellerer H, Pferschy U, Pisinger D (2004) Knapsack Problems (Springer, Berlin).Crossref, Google Scholar
• Martello S, Toth P (1977) An upper bound for the zero-one knapsack problem and a branch and bound algorithm. Eur. J. Oper. Res. 1(3):169–175.Crossref, Google Scholar
• Martello S, Toth P (1988) A new algorithm for the 0-1 knapsack problem. Management Sci. 34(5):633–644.Link, Google Scholar
• Martello S, Toth P (1990) Knapsack Problems (Wiley and Sons, Chichester, UK).Google Scholar
• Mersha AG, Dempe S (2006) Linear bilevel programming with upper level constraints depending on the lower level solution. Appl. Math. Comput. 180(1):247–254.Google Scholar
• Nikoofal ME, Zhuang J (2012) Robust allocation of a defensive budget considering an attacker’s private information. Risk Anal.: Internat. J. 32(5):930–943.Crossref, Google Scholar
• Nikoofal ME, Zhuang J (2015) On the value of exposure and secrecy of defense system: First-mover advantage vs. robustness. Eur. J. Oper. Res. 246(1):320–330.Crossref, Google Scholar
• Özaltın OY, Propkopyev OA, Schaefer AJ (2010) The bilevel knapsack problem with stochastic right-hand sides. Oper. Res. Lett. 38(4):328–333.Crossref, Google Scholar
• Pardalos PM, Resende MG (2002) Handbook of Applied Optimization (Oxford University Press, New York).Crossref, Google Scholar
• Ren S, Zeng B, Qian X (2013) Adaptive bilevel programming for optimal gene knockouts for targeted overproduction under phenotypic constraints. BMC Bioinformatics 14(Suppl 2):Article S17.Crossref, Google Scholar
• Samuel A, Guikema SD (2012) Resource allocation for homeland defense: Dealing with the team effect. Decision Anal. 9(3):238–252.Link, Google Scholar
• Shan X, Zhuang J (2013) Hybrid defensive resource allocations in the face of partially strategic attackers in a sequential defender-attacker game. Eur. J. Oper. Res. 228(1):262–272.Crossref, Google Scholar
• Shen S, Smith JC, Goli R (2012) Exact interdiction models and algorithms for disconnecting networks via node deletions. Discrete Optim. 9(3):172–188.Crossref, Google Scholar
• Smith JC, Lim C, Sudargho F (2007) Survivable network design under optimal and heuristic interdiction scenarios. J. Global Optim. 38(2):181–199.Crossref, Google Scholar
• Tahernejad S, DeNegre S, Ralphs T (2016) A branch-and-cut algorithm for mixed integer bilevel linear optimization problems and its implementation. Technical Report 16T-015-R3, Lehigh University, Bethlehem, PA.Google Scholar
• Tang Y, Richard J, Smith J (2015) A class of algorithms for mixed-integer bilevel min–max optimization. J. Global Optim. 66:225–262.Crossref, Google Scholar
• Toth P (1980) Dynamic programming algorithms for the zero-one knapsack problem. Computing 25(1):29–45.Crossref, Google Scholar
• Vicente LN, Savard G, Judice J (1996) Discrete linear bilevel programming problem. J. Optim. Theory Appl. 89(3):597–614.Crossref, Google Scholar
• Wood R (1993) Deterministic network interdiction. Math. Comput. Model. 17(2):1–18.Crossref, Google Scholar
• Zare MH, Borrero JS, Zeng B, Prokopyev OA (2019) A note on linearized reformulations for a class of bilevel linear integer problems. Ann. Oper. Res. 272(1–2):99–117.Crossref, Google Scholar
• Zare MH, Özaltın OY, Prokopyev OA (2018) On a class of bilevel linear mixed-integer programs in adversarial settings. J. Global Optim. 71(1):91–113.Crossref, Google Scholar
• Zhang J, Zhuang J, Behlendorf B (2018) Stochastic shortest path network interdiction with a case study of arizona–mexico border. Reliability Engrg. System Safety 179:62–73.Crossref, Google Scholar
• Zheng Y, Wan Z, Jia S, Wang G (2015) A new method for strong-weak linear bilevel programming problem. J. Indust. Management Optim. 11(2):529–547.Crossref, Google Scholar