Learning in Sequential Bilevel Linear Programming

References

• Ahmed S, Guan Y (2005) The inverse optimal value problem. Math. Programming 102(1):91–110.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.Google Scholar
• Bayrak H, Bailey M (2008) Shortest path network interdiction with asymmetric information. Networks 52(3):133–140.Google Scholar
• Ben-Tal A, El Ghaoui L, Nemirovski A (2009) Robust Optimization (Princeton University Press, NJ).Google Scholar
• Bertsimas D, Dunning I (2016) Multistage robust mixed-integer optimization with adaptive partitions. Oper. Res. 64(4):980–998.Link, Google Scholar
• Bertsimas D, Georghiou A (2015) Design of near optimal decision rules in multistage adaptive mixed-integer optimization. Oper. Res. 63(3):610–627.Link, Google Scholar
• Borrero JS, Prokopyev OA, Sauré D (2016) Sequential shortest path interdiction with incomplete information. Decision Anal. 13(1):68–98.Link, Google Scholar
• Borrero JS, Prokopyev OA, Sauré D (2019) Sequential interdiction with incomplete information. Oper. Res. 67(1):72–89.Link, Google Scholar
• Brown G, Carlyle M, Salmerón J, Wood K (2006) Defending critical infrastructure. Interfaces 36(6):530–544.Link, Google Scholar
• Buehn A, Eichler S (2009) Smuggling illegal vs. legal goods across the U.S.-Mexico border: A structural equations model approach. Southern Econom. J. 76(2):328–350.Google Scholar
• Cao D, Chen M (2006) Capacitated plant selection in a decentralized manufacturing environment: A bilevel optimization approach. Eur. J. Oper. Res. 169(1):97–110.Google Scholar
• Cesa-Bianchi N, Lugosi G (2006) Prediction, Learning, and Games (Cambridge University Press, New York).Google Scholar
• Cesa-Bianchi N, Lugosi G (2012) Combinatorial bandits. J. Comput. System Sci. 78(5):1404–1422.Google Scholar
• Chern M, Lin K (1995) Interdicting the activities of a linear program: A parametric analysis. Eur. J. Oper. Res. 86(3):580–591.Google Scholar
• Colson B, Marcotte P, Savard G (2005) Bilevel programming: A survey 4OR 3(2):87–107.Google Scholar
• Colson B, Marcotte P, Savard G (2007) An overview of bilevel optimization. Ann. Oper. Res. 153(1):235–256.Google Scholar
• Côté J-P, Marcotte P, Savard G (2003) A bilevel modelling approach to pricing and fare optimisation in the airline industry. J. Revenue Pricing Management 2(1):23–36.Google Scholar
• Dempe S (2002) Foundations of Bilevel Programming (Springer Science & Business Media, Boston).Google Scholar
• Fudenberg D, Levine D (1998) The Theory of Learning in Games, vol. 1, 1st ed. (The MIT Press, Cambridge, MA).Google Scholar
• Gathmann C (2008) Effects of enforcement on illegal markets: Evidence from migrant smuggling along the southwestern border. J. Public Econom. 92(10–11):1926–1941.Google Scholar
• Gorelick N, Hancher M, Dixon M, Ilyushchenko S, Thau D, Moore R (2017) Google Earth engine: Planetary-scale geospatial analysis for everyone, Remote Sensing of Environment. 202:18–27.Google Scholar
• Hemmecke R, Schultz R, Woodruff DL (2003) Interdicting stochastic networks with binary interdiction effort. Woodruff DL, ed. Network Interdiction and Stochastic Integer Programming Oper. Res/Comput. Sci. Interfaces Series, vol. 22 (Springer, Boston), 69–84.Google Scholar
• Israeli E, Wood R (2002) Shortest-path network interdiction. Networks 40(2):97–111.Google Scholar
• Lim C, Smith JC (2007) Algorithms for discrete and continuous multicommodity flow network interdiction problems. IIE Trans. 39(1):15–26.Google Scholar
• Lorca Á, Sun XA, Litvinov E, Zheng T (2016) Multistage adaptive robust optimization for the unit commitment problem. Oper. Res. 64(1):32–51.Link, Google Scholar
• Lucotte M, Nguyen S (2013) Equilibrium and Advanced Transportation Modelling (Springer Science & Business Media, Boston).Google Scholar
• Magliocca NR, McSweeney K, Sesnie SE, Tellman E, Devine JA, Nielsen EA, Pearson Z, Wrathall DJ (2019) Modeling cocaine traffickers and counterdrug interdiction forces as a complex adaptive system. Proc. Natl. Acad. Sci. USA 116(16):7784–7792.Google Scholar
• McCormick GP (1976) Computability of global solutions to factorable nonconvex programs: Part I—Convex underestimating problems. Math. Programming 10(1):147–175.Google Scholar
• Modaresi S, Sauré D, Vielma J (2020) Learning in combinatorial optimization: What and how to explore. Oper. Res. 68(5):1585–1604.Link, Google Scholar
• Robbins H (1952) Some aspects of the sequential design of experiments. Bull. Amer. Math. Soc. 58(5):527–535.Google Scholar
• Sherali HD, Soyster AL, Murphy FH (1983) Stackelberg-Nash-Cournot equilibria: Characterizations and computations. Oper. Res. 31(2):253–276.Link, Google Scholar
• Smith JC, Song Y (2020) A survey of network interdiction models and algorithms. Eur. J. Oper. Res. 283(3):797–811.Google Scholar
• Steinrauf R (1991) Network interdiction models. Unpublished PhD thesis, Naval Postgraduate School, Monterey, CA.Google Scholar
• Unsal O (2010) Two-person zero-sum network-interdiction game with multiple inspector types. Technical report, Naval Postgraduate School, Monterey, CA.Google Scholar
• Wood RK (1993) Deterministic network interdiction. Math. Comput. Model. 17(2):1–18.Google Scholar
• Yang J, Borrero JS, Prokopyev OA, Sauré D (2021) Sequential shortest path interdiction with incomplete information and limited feedback. Decision Anal. 18(3):218–244.Google Scholar
• Yürekli A, Sayginsoy Ö (2010) Worldwide organized cigarette smuggling: An empirical analysis. Appl. Econom. 42(5):545–561.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.Google Scholar