A Value-Function-Based Exact Approach for the Bilevel Mixed-Integer Programming Problem
Published Online:11 Apr 2017https://doi.org/10.1287/opre.2017.1589
References
- (1972) Canonical cuts on the unit hypercube. SIAM J. Appl. Math. 23(1):61–69.Crossref, Google Scholar
- (1983) An efficient point algorithm for a linear two-stage optimization problem. Oper. Res. 31(4):670–684.Link, Google Scholar
- (1992) An algorithm for the discrete bilevel programming problem. Naval Res. Logist. 39(3):419–435.Crossref, Google Scholar
- (2009) Bilevel optimization formulation for parameter estimation in vapor–liquid (–liquid) phase equilibrium problems. Chemical Engrg. Sci. 64(8):1768–1783.Crossref, Google Scholar
- (2001) A bilevel model for toll optimization on a multicommodity transportation network. Transportation Sci. 35(4):345–358.Link, Google Scholar
- (2003) Optknock: A bilevel programming framework for identifying gene knockout strategies for microbial strain optimization. Biotechnology and Bioengineering 84(6):647–657.Crossref, Google Scholar
- (1982) A linear two-level programming problem. Comput. Oper. Res. 9(1):59–76.Crossref, Google Scholar
- (2015) Robust multistage decision making. Aleman DM, Thiele AC, eds. Tutorials in Operations Research (INFORMS, Catonsville, MD), 20–46.Link, Google Scholar
- (2016) On the solution of convex bilevel optimization problems. Computational Optim. Appl. 63(3):685–703.Crossref, Google Scholar
- (2015) Necessary optimality conditions for optimistic bilevel programming problems using set-valued programming. J. Global Optim. 61(4):769–788.Crossref, Google Scholar
- (2012) Bilevel road pricing: Theoretical analysis and optimality conditions. Ann. Oper. Res. 196(1):223–240.Crossref, Google Scholar
- (2013) The bilevel programming problem: Reformulations, constraint qualifications and optimality conditions. Math. Programming 138(1):1–27.Google Scholar
- (2014) KKT reformulation and necessary conditions for optimality in nonsmooth bilevel optimization. SIAM J. Optim. 24(4):1639–1669.Crossref, Google Scholar
- (2007) New necessary optimality conditions in optimistic bilevel programming. Optimization 56(5–6):577–604.Crossref, Google Scholar
- (2005) Discrete bilevel programming: Application to a natural gas cash-out problem. Eur. J. Oper. Res. 166(2):469–488.Crossref, Google Scholar
- (2014) Necessary optimality conditions in pessimistic bilevel programming. Optimization 63(4):505–533.Crossref, Google Scholar
- (2011) Natural gas bilevel cash-out problem: convergence of a penalty function method. Eur. J. Oper. Res. 215(3):532–538.Crossref, Google Scholar
- (2015) Bilevel Programming Problems (Springer, Berlin).Crossref, Google Scholar
- (2009) A branch-and-cut algorithm for integer bilevel linear programs. Chinneck JW, Kristjansson B, Saltzman MJ, eds. Operations Research and Cyber-Infrastructure (Springer, New York), 65–78.Crossref, Google Scholar
- (2010) Multiparametric programming based algorithms for pure integer and mixed-integer bilevel programming problems. Comput. Chemical Engrg. 34(12):2097–2106.Crossref, Google Scholar
- (2007) Parametric global optimisation for bilevel programming. J. Global Optim. 38(4):609–623.Crossref, Google Scholar
- (2009) Bilevel programming with discrete lower level problems. Optimization 58(8):1029–1047.Crossref, Google Scholar
- (2013) Robust counterparts of inequalities containing sums of maxima of linear functions. Eur. J. Oper. Res. 277(1):30–43.Crossref, Google Scholar
- (1992) New branch-and-bound rules for linear bilevel programming. SIAM J. Scientific Statist. Comput. 13(5):1194–1217.Crossref, Google Scholar
- (2016) A mixed-integer bilevel programming approach for a competitive prioritized set covering problem. Discrete Optim. 20:105–134.Crossref, Google Scholar
- (2002) Shortest-path network interdiction. Networks 40(2):97–111.Crossref, Google Scholar
- (2010) A linearization approach to solve the natural gas cash-out bilevel problem. Ann. Oper. Res. 181(1):423–442.Crossref, Google Scholar
- (2010) Parametric integer programming algorithm for bilevel mixed integer programs. J. Optim. Theory Appl. 146(1):137–150.Crossref, Google Scholar
- (1998) A bilevel model of taxation and its application to optimal highway pricing. Management Sci. 44(12):1608–1622.Link, Google Scholar
- (2016) A backward sampling framework for interdiction problems with fortification. INFORMS J. Comput. 29(1):123–139.Link, Google Scholar
- (1995) Bilevel programming in traffic planning: Models, methods and challenge. J. Global Optim. 7(4):381–405.Crossref, Google Scholar
- (2010) Global solution of nonlinear mixed-integer bilevel programs. J. Global Optim. 47(4):557–582.Crossref, Google Scholar
- (2009a) Bilevel optimization formulation for parameter estimation in liquid–liquid phase equilibrium problems. Chemical Engrg. Sci. 64(3):548–559.Crossref, Google Scholar
- (2009b) Model and parameter identification in phase equilibria. Comput. Aided Chemical Engrg. 26:597–601.Crossref, Google Scholar
- (2008) Global solution of bilevel programs with a nonconvex inner program. J. Global Optim. 42(4):475–513.Crossref, Google Scholar
- (1968) A n job, one machine sequencing algorithm for minimizing the number of late jobs. Management Sci. 15(1):102–109.Link, Google Scholar
- (1990) The mixed integer linear bilevel programming problem. Oper. Res. 38(5):911–921.Link, Google Scholar
- (2013) Procurement allocation planning with multiple suppliers under competition. Internat. J. Production Res. 51(23–24):6900–6922.Crossref, Google Scholar
- (2009) Resolution method for mixed integer bi-level linear problems based on decomposition technique. J. Global Optim. 44(1):29–51.Crossref, Google Scholar
- (2005) An extended Kuhn-Tucker approach for linear bilevel programming. Appl. Math. Comput. 162(1):51–63.Crossref, Google Scholar
- (2006) An extended branch and bound algorithm for linear bilevel programming. Appl. Math. Comput. 180(2):529–537.Crossref, Google Scholar
- (2009) A global optimization algorithm for generalized semi-infinite, continuous minimax with coupled constraints and bi-level problems. J. Global Optim. 44(2):235–250.Crossref, Google Scholar
- (1993) A global optimization approach for the linear two-level program. J. Global Optim. 3(1):1–23.Crossref, Google Scholar
- (2013) Pessimistic bilevel optimization. SIAM J. Optim. 23(1):353–380.Crossref, Google Scholar
- (1993) Deterministic network interdiction. Math. Comput. Model. 17(2):1–18.Crossref, Google Scholar
- (2012) A bi-level model for location-allocation problem of construction and demolition waste management under fuzzy random environment. Internat. J. Civil Engrg. 10(1):1–12.Google Scholar
- (2014) An exact algorithm for the bilevel mixed integer linear programming problem under three simplifying assumptions. Comput. Oper. Res. 41(1):309–318.Crossref, Google Scholar
- (2012) Bilevel optimization of regional water resources allocation problem under fuzzy random environment. J. Water Resources Planning and Management 139(3):246–264.Crossref, Google Scholar
- (2006) Constraint qualifications and KKT conditions for bilevel programming problems. Math. Oper. Res. 31(4):811–824.Link, Google Scholar
- (1995) Optimality conditions for bilevel programming problems. Optimization 33(1):9–27.Crossref, Google Scholar

