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# Bilevel and multilevel programming: A bibliography review

J. Global Optimization, no. 3 (1994): 291-306

EI

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摘要

This paper contains a bibliography of all references central to bilevel and multilevel programming that the authors know of. It should be regarded as a dynamic and permanent contribution since all the new and appropriate references that are brought to our attention will be periodically added to this bibliography. Readers are invited to su...更多

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简介

**Introduction and Historical Notes**

Multilevel optimization problems are mathematical programs which have a subset of their variables constrained to be an optimal solution of other programs parameterized by their remaining variables.- The bilevel programming problem (BPP) is defined as: min F(x, y)
- - the linear-quadratic BPP, where the lower level objective is a convex quadratic and all remaining functions are affine.
- This result established that any integer or concave quadratic program could be written as a linear BPP.

重点内容

**Introduction and Historical Notes**

Multilevel optimization problems are mathematical programs which have a subset of their variables constrained to be an optimal solution of other programs parameterized by their remaining variables- This result established that any integer or concave quadratic program could be written as a linear bilevel programming problem (BPP)
- Llnlti [143]), none have succeeded far in proposing conditions that guarantee that the optimal solution of a given bilevel program is Pareto-optimal or efficient [79] for both upper and lower level objective functions (W
- Anandalingam exploit the penalized bilinear version of a linear BPP and introduce a exact penalty function algorithm that finds a global solution of the linear BPP by solVing a sequence of bilinear programs
- The subjects covered in this bibliography review are bilevel and multilevel programming and Stackelberg problems when considered as optimization problems - usually called static Stackelberg problems

结果

- This is not entirely possible since the reciprocal result states that there exists a bilinear program whose optimal solutions are global solutions of the corresponding linear BPP.
- Llnlti [143]), none have succeeded far in proposing conditions that guarantee that the optimal solution of a given bilevel program is Pareto-optimal or efficient [79] for both upper and lower level objective functions (W.
- Other two-level optimization problems might be confused with bilevel programs.
- Authors who have studied generalized bilevel programming problems include T.
- The algorithms that have been proposed for solving continuous bilevel programming problems may be divided in five different classes.
- Karwan [35] have proposed algorithms that compute global solutions of linear BPPs by enumerating the extreme points of f~.
- Savard [76] have proposed a branch and bound algorithm for the solution of the linear BPP that seems efficient for the solution of medium-scale problems.
- Yang [154] have proposed branch and bound procedures for the solution of integer linear instances of the BPP, and T.
- J~dice [146] studied the application of this algorithm to convex bilevel programming, where the lower level problems are strictly convex quadratic programs, and proposed appropriate stepsize rules to displacements along directions in the induced region.
- Lasdon [92] for the solution of nonlinear BPPs. This algorithm consists of applying gradient information to the implicit optimization problem: min F(x, y(x)) X
- Wu [101] for the derivation of an exact penalty function that only uses the square-root of the complementarity term associated with the lower level quadratic program as the penalty term.

结论

- Anandalingam exploit the penalized bilinear version of a linear BPP and introduce a exact penalty function algorithm that finds a global solution of the linear BPP by solVing a sequence of bilinear programs.
- Chen [70, 71] and R.L. Tobin and T.L. Friesz [141]).
- Bilevel programming can provide a novel approach for analyzing the step selection subproblem in a trust region algorithm for nonlinear equality constrained optimization, and has been applied to the discriminant problem [107].
- The subjects covered in this bibliography review are bilevel and multilevel programming and Stackelberg problems when considered as optimization problems - usually called static Stackelberg problems.

引用论文

- E. Aiyoshi and K. Shimizu. Hierarchical decentralized systems and its new solution by a barrier method. IEEE Transactions on Systems, Man, and Cybernetics, 11:444-449, 1981.
- E. Aiyoshi and K. Shimizu. A solution method for the static constrained Stackelberg problem via penalty method. IEEE Transactions on Automatic Control, 29:1111-1114, 1984.
- E AI-Khayyal, R. Horst, and P. Pardalos. Global optimization of concave functions subject to quadratic constraints: an application in nonlinear bilevel programming. Annals of Operations Research, 34:125-147, 1992.
- G. Anandalingam. An analysis of information and incentives in bi-levelprogramming. In IEEE 1985 Proceedings of the International Conference on Cybernetics and Society, pages 925-929, 1985.
- G. Anandalingam. A mathematical programming model of decentralized multi-level systems. Journal of the Operational Research Society, 39:1021-1033, 1988.
- G. Anandalingam and V. Aprey. Multi-level programming and conflict resolution. European Journal of Operational Research, 51:233-247, 1991.
- G. Anandalingam and T. Friesz. Hierarchical optimization: an introduction. Annals of Operations Research, 34:1-11, 1992.
- G. Anandalingam, R. Mathieu, L. Pittard, and N. Sinha. Artificialintelligencebased approaches for solving hierarchical optimization problems. In R. Sharda, B. Golden, E. Wasil, O. Balci and W. Stewart, editor, Impacts of Recent Computer Advances on Operations Research, pages 289-301. Elsevier Science Publishing Co., Inc., 1983.
- G. Anandalingam and D. White. A solution method for the linear static Stackelberg problem using penalty functions. IEEE Transactions on Automatic Control, 35:1170-1173, 1990.
- J. Bard. A grid search algorithm for the linear bilevel programming problem. In Proceedings of the 14th Annual Meeting of the American Institutefor Decision Science, pages 256--258, 1982.
- J. Bard. An algorithm for solving the general bilevel programming problem. Mathematics of Operations Research, 8:260-272, 1983.
- J. Bard. Coordination of a multidivisional organization through two levels of management. OMEGA, 11:457-468, 1983.
- J. Bard. An efficient point algorithm for a linear two-stage optimization problem. Operations Research, 31:670-684, 1983.
- J. Bard. An investigation of the linear three level programming problem. IEEE Transactions on Systems, Man, and Cybernetics, 14:711-717, 1984.
- J. Bard. Optimality conditions for the bilevel programming problem. Naval Research Logistics Quarterly, 31:13-26, 1984.
- J. Bard. Geometric and algorithm developments for a hierarchical planning problem. European Journal of Operational Research, 19:372-383, 1985.
- J. Bard. Convex two-level optimization. Mathematical Programming, 40:15-27, 1988.
- J. Bard. Some properties of the bilevel programming problem. Journal of Optimization Theory and Applications, 68:371-378, 1991. Technical Note.
- J. Bard and J. Faik. An explicit solution to the multi-level programming problem. Computers and Operations Research, 9:77-100, 1982.
- J. Bard and J. Moore. A branch and bound algorithm for the bilevel programming problem. SIAM Journal on Scientific and Statistical Computing, 11:281-292, 1990.
- J. Bard and J. Moore. An algorithm for the discrete bilevel programming problem. Naval Research Logistics, 39:419-435, 1992.
- O. Ben-Ayed. Bilevel linear programming: analysis and application to the network design problem. PhD thesis, University of Illinois at Urbana-Champaign, 1988.
- O. Ben-Ayed. A bilevel linear programming model applied to the Tunisian inter-regional network design problem. Revue Tunisienne d'~conomie et de Gestion, 5:235-279, 1990.
- O. Ben-Ayed. Bilevel linear programming. Computers and Operations Research, 20:485-501, 1993.
- O.Ben-AyedandC.Blair. Computationaldifficultiesofbilevellinearprogramming.Operations Research, 38:556--560, 1990.
- O. Ben-Ayed, C. Blair, D. Boyce, and L. LeBlanc. Construction of a real-world bilevel linear programming model of the highway design problem. Annals of Operations Research, 34:219-
- O. Ben-Ayed, D. Boyce, and C. Blair. A general bilevel linear programming formulation of the network design problem. Transportation Research, 22 B:311-318, 1988.
- H. Benson. On the structure and properties of a linear multilevel programming problem. Journal of Optimization Theory and Applications, 60:353-373, 1989.
- Z. Bi. Numerical methods for bilevel programming problems. PhD thesis, Department of Systems Design Engineering, University of Waterloo, 1992.
- Z. Bi and E Calamai. Optimality conditions for a class of bilevel programming problems. Technical Report #191-O-191291, Department of Systems Design Engineering, University of Waterloo, 1991.
- Z. Bi, P. Calamai, and A. Conn. An exact penalty function approach for the linear bilevel programming problem. Technical Report #167-O-310789, Department of Systems Design Engineering, University of Waterloo, 1989.
- Z. Bi, P. Calamai, and A. Conn. An exact penalty function approach for the nonlinear bilevel programming problem. Technical Report #180-O-170591, Department of Systems Design Engineering, University of Waterloo, 1991.
- W. Bialas and M. Karwan. Multilevel linear programming. Technical Report 78-1, Operations Research Program, State University of New York at Buffalo, 1978.
- W. Bialas and M. Karwan. On two-level optimization. IEEE Transactions on Automatic Control, 27:211-214, 1982.
- W. Bialas and M. Karwan. Two-level linear programming. Management Science, 30:10041020, 1984.
- W. Bialas, M. Karwan, and J. Shaw. A parametric complementary pivot approach for two-level linear programming. Technical Report 80-2, Operations Research Program, State University of New York at Buffalo, 1980.
- J. Bisschop, W. Candler, J. Duloy, and G. O'Mara. The indus basin model: a special application of two-level linear programming. Mathematical Programming Study, 20:30-38, 1982.
- C. Blair. The computational complexity of multi-level linear programs. Annals of Operations Research, 34:13-19, 1992.
- J. Bracken, J. Falk, andJ. McGill. Equivalence oftwomathematicalprograms with optimization problems in the constraints. Operations Research, 22:1102-1104, 1974.
- J. Bracken and J. McGill. Mathematical programs with optimizationproblems in the constraints. Operations Research, 21:37-44, 1973.
- J. Bracken and J. McGill. Defense applications of mathematical programs with optimization problems in the constraints. Operations Research, 22:1086-1096, 1974.
- J. Bracken and J. McGill. A method for solving mathematical programs with nonlinear programs in the constraints. Operations Research, 22:1097-1101, 1974.
- J. Bracken and J. McGill. Production and marketing decisions with multiple objectives in a competitive environment. Journal of Optimization Theory and Applications, 24:449-458, 1978.
- P. Calamai and L. Vicente. Generating linear and linear-quadratic bilevel programming problems. SIAM Journal on Scientific and Statistical Computing, 14:770-782, 1993.
- E Calamai and L. Vicente. Algorithm 728: Fortran subroutines for generating quadratic bilevel programming problems. A CM Transactions on Mathematical Software, 20:120-123, 1994.
- E Calamai and L. Vicente. Generating quadratic bilevel programming problems. ACM Transactions on Mathematical Software, 20:103-119, 1994.
- W. Candler. A linear bilevel programming algorithm: A comment. Computers and Operations Research, 15:297-298, 1988.
- W. Candler, J. Fortuny-Amat, and B. McCafl. The potential role of multilevel programming in agricultural economics. American Journal of Agricultural Economics, 63:521-531,1981.
- W. Candler and R. Norton. Multilevel programming. Technical Report 20, World Bank Development Research Center, Washington D.C., 1977.
- W. Candler and R. Norton. Multilevel programming and development policy. Technical Report 258, World Bank Staff, Washington D.C., 1977.
- W. Candler and R. Townsley. A linear two-level programming problem. Computers and Operations Research, 9:59-76, 1982.
- R. Cassidy, M. Kirby, and W. Raike. Efficient distribution of resources through three levels of govemment. Management Science, 17:462-473, 1971.
- M. Cellis,J. Dennis, and R. Tapia. A trust region strategy for nonlinear equality constrained optimization. In Numerical Optimization 1984, Proceedings 20, pages 71-82. SIAM, Philadelphia, 1985.
- Y. Chert. Bilevel programming problems: analysis, algorithms and applications. PhD thesis, Universit6 de Montr6al, 1993.
- Y. Chert and M. Florian. The nonlinear bilevel programming problem: a general formulation and optimality conditions. Technical Report CRT-794, Centre de Recherche sur les Transports, 1991.
- Y. Chen and M. Florian. On the geometry structure of linear bilevel programs: a dual approach. Technical Report CRT-867, Centre de Recherche sur les Transports, 1992.
- Y. Chert and M. Florian. The nonlinear bilevel programming problem: formulations, regularity and optimality conditions. Technical Report CRT-794, Centre de Recherche sur les Transports, 1993.
- Y. Chen, M. Florian, and S. Wu. A descent dual approach for linear bilevel programs. Technical Report CRT-866, Centre de Recherche sur les Transports, 1992.
- E Clarke and A. Westerberg. A note on the optimality conditions for the bilevel programming problem. Naval Research Logistics, 35:413-418, 1988.
- S. Dempe. A simple algorithm for the linear bilevel programming problem. Optimization, 18:373-385, 1987.
- S. Dempe. On one optimality condition for bilevel optimization. Vestnik Leningrad Gos. University, pages 10-14, 1989. Serija I, in Russian, translation Vestnik Leningrad University, Math., 22:11-16, 1989.
- S. Dempe. A necessary and a sufficient optimalitycondition for bilevel programming problems. Optimization, 25:341-354, 1992.
- S. Dempe. Optimality conditions for bilevel programming problems. In E Kall, editor, System modelling and optimization, pages 17-24. Springer-Verlag, 1992.
- A. deSilva. Sensitivityformulasfornonlinearfactorableprogrammingandtheirapplicationto the solution of an implicitly defined optimization model of US crude oilproduction. PhD thesis, George Washington University, 1978.
- A. deSilva and G. McCormick. Implicitlydefined optimizationproblems. Annals of Operations Research, 34:107-124, 1992.
- Y. Dirickx and L. Jennegren. Systems analysis by multi-level methods: with applications to economics and management. John Wiley, New York, 1979.
- T. Edmunds. Algorithmsfor nonlinear bilevel mathematicalprograms. PhD thesis, Department of Mechanical Engineering, University of Texas at Austin, 1988.
- T. Edmunds and J. Bard. Algorithms for nonlinear bilevel mathematical programming. IEEE Transactions on Systems, Man, and Cybernetics, 21:83-89, 1991.
- T. Edmunds and J. Bard. An algorithm for the mixed-integer nonlinear bilevel programming problem. Annals of Operations Research, 34:149-162, 1992.
- M. Florian and Y. Chen. A bilevel programming approach to estimating O-D matrix by traffic counts. Technical Report CRT-750, Centre de Recherche sur les Transports, 1991.
- M. Florian and Y. Chen. A coordinate descent method for bilevel O-D matrix estimation problems. Technical Report CRT-807, Centre de Recherche sur les Transports, 1993.
- J. Fortuny-Amat and B. McCad. A representation and economic interpretation of a two-level programming problem. Journal of the OperationalResearch Society, 32:783-792, 1981.
- T. Friesz, C. Suwansirikul, and R. Tobin. Equilibrium decomposition optimization: a heuristic for the continuous equilibrium network design problem. TransportationScience, 21:254-263, 1987.
- T. Friesz, R. Tobin, H. Cho, and N. Mehta. Sensitivity analysis based heuristic algorithms for mathematical programs with variational inequality constraints. Mathematical Programming, 48:265-284, 1990.
- G. Gallo and A. Ulkticti. Bilinear programming: an exact algorithm. Mathematical Programming, 12"173-194, 1977. BILEVELAND MULTILEVELPROGRAMMING:A BIBLIOGRAPHYREVIEW
- E Hansen, B. Jaumard, and G. Savard. New branch-and-bound rules for linear bilevel programming. SIAM Journal on Scientific and Statistical Computing, 13:1194-1217, 1992.
- E Harker and J.-S. Pang. Existence of optimal solutions to mathematical programs with equilibrium constraints. Operations Research Letters, 7:61-64, 1988.
- A. Haurie, R. Loulou, and G. Savard. A two-levelsystems analysismodel of power cogeneration under asymmetric pricing. Technical Report G-89-34, Groupe d't~tudes et de Recherche en Analyse des D6cisions, 1989.
- A. Haurie, G. Savard, and D. White. A note on: an efficientpoint algorithm for a linear two-stage optimization problem. Operations Research, 38:553-555, 1990.
- B. Hobbs and S. Nelson. A nonlinear bilevel model for analysis of electric utility demand-side planning issues. Annals of Operations Research, 34:255-274, 1992.
- Y. Ishizuka. Optimality conditions for quasi-differentiableprograms with applications to twolevel optimization. SlAM Journal on Control and Optimization, 26:1388-1398, 1988.
- Y. Ishizuka and E. Aiyoshi. Double penalty method for bilevel optimization problems. Annals of Operations Research, 34:73-88, 1992.
- R. Jan and M. Chem. Multi-level nonlinear integer programming. 1990. (Preprint from the Department of Computer and Information Science, National Chiao Tung University).
- R. Jeroslow. The polynomial hierarchy and a simple model for competitive analysis. Mathematical Programming, 32:146-164, 1985.
- J. Jtidice and A. Faustino. The solution of the linear bilevel programming problem by using the linear complementarity problem. Investiga~ao Operacional, 8:77-95, 1988.
- J. Jtidice and A. Faustino. A sequential LCP method for bilevel linear programming. Annals of Operations Research, 34:89-106, 1992.
- J. Jtfdice and A. Faustino. The linear-quadratic bilevel programming problem. INFOR, 32:8798, 1994.
- T. Kim and S. Suh. Toward developing a national transportation planning model: a bilevel programming approach for Korea. Annals of Regional Science, 22:65-80, 1988.
- M. Kocvara and J. Outrata. A nondifferentiable approach to the solution of optimum design problems with variational inequalities. In P. Kall, ed., System Modelling and Optimization, Lecture Notes in Control and Information Sciences 180, pages 364-373. Springer-Veflag, Berlin, 1992.
- M. Kocvara and J. Outrata. A numerical solution of two selected shape optimization problems. Technical Report DFG (German Scientific Foundation) Research Report 464, University of Bayreuth, 1993.
- C. Kolstad. A review of the literature on bi-levelmathematical programming. Technical Report LA-10284-MS, US-32, Los Alamos National Laboratory, 1985.
- C. Kolstad and L. Lasdon. Derivative evaluation and computational experience with large bilevel mathematical programs. Journal of Optimization Theory and Applications, 65:485499, 1990.
- M. Labb6, P. Marcotte, and G. Savard. A bilevel model of taxation and its applicationto optimal highway policy. 1993. Preprint.
- L. Leblanc and D. Boyce. A bilevel programming algorithm for exact solution of the network design problem with user-optimal flows. Transportation Research, 20 B:259-265, 1986.
- P. Loridan and J. Morgan. Approximate solutions for two-level optimization problems. In K. Hoffman, J. Hiriart-Urruty, C. Lamerachal and J. Zowe, editor, Trends in Mathematical Optimization, volume 84 of International Series of Numerical Mathematics, pages 181-196. Birkh~iuser Verlag, Basel, 1988.
- P. Loridan and J. Morgan. A theoretical approximation scheme for Stackelberg problems. Journal of Optimization Theory and Applications, 61:95-110, 1989.
- P. Loridan and J. Morgan. e-Regularized two-level optimization problems: approximation and existence results, In Optimization - Fifth French-German Conference, Lecture Notes in Mathematics 1405, pages 99-113. Springer-Veflag, Berlin, 1989.
- E Loridan and J. Morgan. New results on approximate solutions in two-level optimization. Optimization, 20:819-836, 1989.
- E Loridan and J. Morgan. Quasi convex lower level problem and applications in two level optimization, volume 345 of Lecture Notes in Economics and Mathematical Systems, pages 325-341. Springer-Vedag, Berlin, 1990.
- ELuh, T.-S.Chang, andT.Ning. Three-levelStackelbergdecisionproblems.IEEETransactions on Automatic Control, 29:280-282, 1984.
- Z.-Q. Luo, J.-S. Pang, and S. Wu. Exact penalty functions for mathematical programs and bilevel programs with analytic constraints. 1993. Preprint from the Department of Electrical and Computer Engineering, McMaster University.
- P. Marcotte. Network optimizationwith continuous controlparameters. TransportationScience, 17:181-197, 1983.
- E Marcotte. Network design problem with congestion effects: a case of bilevel programming. Mathematical Programming, 34:142-162, 1986.
- E Marcotte. A note on bilevel programming algorithm by LeBlanc and Boyce. Transportation Research, 22 B:233-237, 1988.
- E Marcotte and G. Marquis. Efficient implementation of heuristics for the continuous network design problem. Annals of OperationsResearch, 34:163-176, 1992.
- E Marcotte and G. Savard. A note on the pareto optimality of solutions to the linear bilevel programming problem. Computersand OperationsResearch, 18:355-359, 1991.
- E Marcotte and G. Savard. Novel approaches to the discrimination problem. ZOR - Methods and Models of OperationsResearch, 36:517-545, 1992.
- E Marcotte and D. Zhu. Exact and inexact penalty methods for the generalized bilevel programming problem. Technical Report CRT-920, Centre de Recherche sur les Transports, 1992.
- R. Mathieu, L. Pittard, and G. Anandalingam. Genetic algorithm based approach to bi-level linear programming. RAIRO: Recherche Operationelle,(forthcoming).
- M. Mesanovic, D. Macko, and Y. Takahara. Theory of hierarchical, multilevel systems. Academic Press, New York and London, 1970.
- T. Miller, T. Friesz, and R. Tobin. Heuristic algorithms for delivered price spatially competitive network facility location problems. Annals of OperationsResearch, 34:177-202, 1992.
- J. Moore. Extensions to the multilevel linear programming problem. PhD thesis, Department of Mechanical Engineering, University of Texas, Austin, 1988.
- J. Moore and J. Bard. The mixed integer linear bilevel programming problem. Operations Research, 38:911-921, 1990.
- S. Narula and A. Nwosu. A dynamic programming solution for the hierarchical linear programming problem. Technical Report 37-82, Department of Operations Research and Statistics, Rensselaer Polytechnic Institute, 1982.
- S. Narula and A. Nwosu. Two-level hierarchical programming problems. In E Hansen, editor, Essays and surveys on multiple criteria decision making, pages 290-299. Springer-Verlag, Berlin, 1983.
- S. Narula and A. Nwosu. An algorithm to solve a two-level resource control pre-emptive hierarchical programming problem. In E Serafini, editor, Mathematics of multiple-objective programming. Springer-Vedag, Berlin, 1985.
- E Neittaanmaki and A. Stachurski. Solving some optimal control problems using the barrier penalty function method. In H.-J. Sebastian and K. Tammer, editors, Proceedings of the 14th IFIP Conference on System Modelling and Optimization, Leipzig 1989, pages 358-367. Springer, 1990.
- A. Nwosu. Pre-emptive hierarchicalprogramming problem: a decentralized decision model. PhD thesis, Department of Operations Research and Statistics,Rensselaer Polytechnic Institute, 1983.
- H. 0nal. Computational experience with a mixed solution method for bilevel linear/quadratic programs. 1992. (Preprint from the University of Illinois at Urbana-Champaign).
- H. Onal. A modified simplex approach for solving bilevel linear programming problems. European Journal of OperationalResearch, 67:126-135, 1993. Models of Operations Research, 34:255-277, 1990.
- 122. J. Outrata. Necessary optimality conditions for Stackelberg problems. Journal of Optimization Theory and Applications, 76:305-320, 1993.
- 123. J. Outrata. On optimization problems with variational inequality constraints. SIAM Journal on Optimization, (forthcoming).
- 124. J. Outrata and J. Zowe. A numerical approach to optimization problems with variational inequality constraints. Technical Report DFG (German ScientificFoundation) Research Report 463, University of Bayreuth, 1993.
- 125. G. Papavassilopoulos. Algorithms for static Stackelberggames with linear costs and polyhedral constraints. In Proceedings of the 21st IEEE Conference on Decisions and Control, pages 647652, 1982.
- 126. F. Parraga. Hierarchical programming and applications to economic policy. PhD thesis, Systems and Industrial Engineering Department, University of Arizona, 1981.
- 127. G. Savard. Contributions d la programmation mathdmatique ?ldeux niveaux. PhD thesis, Ecole Polytechnique, Universit6 de Montr6al, 1989.
- 128. G. Savard and J. Gauvin. The steepest descent direction for the nonlinear bilevel programruing problem. Technical Report G-90-37, Groupe d'I~tudes et de Recherche en Analyse des D6cisions, 1990.
- 129. G. Schenk. A multilevelprogramming model for determining regional effluent charges. Master's thesis, Department of Industrial Engineering, State University of New York at Buffalo, 1980.
- 130. R. Segall. Bi-level geometric programming: a new optimization model. 1989. (Preprint from the Department of Mathematics, University of Lowell Olsen Hall).
- 131. J. Shaw. A parametric complementary pivot approach to multilevel programming. Master's thesis, Department of Industrial Engineering, State University of New York at Buffalo, 1980.
- 132. H. Sherali. A multiple leader Stackelberg model and analysis. Operations Research, 32:390404, 1984.
- 133. K. Shimizu. Two-level decision problems and their new solution methods by a penalty method, volume 2 of Control science and technology for the progress of society, pages 1303-1308. IFAC, 1982.
- 134. K. Shimizu and E. Aiyoshi. A new computational method for Stackelberg and rain-max problems by use of a penalty method. IEEE Transactions on Automatic Control, 26:460-466, 1981.
- 135. K. Shimizu and E. Aiyoshi. Optimality conditions and algorithms for parameter design problems with two-level structure. IEEE Transactions on Automatic Control, 30:986-993, 1985.
- 136. M. Simaan. Stackelberg optimization of two-level systems. IEEE Transactions on Systems, Man, and Cybernetics, 7:554-557, 1977.
- 137. H. Stackelberg. The theory o f the market economy. Oxford University Press, 1952.
- 138. S. Suh and T. Kim. Solving nonlinear bilevel programming models of the equilibrium network design problem: a comparative review. Annals of Operations Research, 34:203-218, 1992.
- 139. C. Suwansirikul, T. Friesz, and R. Tobin. Equilibrium decomposed optimization: a heuristic for the continuous equilibrium network design problem. Transportation Science, 21:254-263, 1987.
- 140. T. Tanino and T. Ogawa. An algorithm for solving two-level convex optimization problems. International Journal of Systems Science, 15:163-174, 1984.
- 141. R. Tobin and T. Friesz. Spatial competition facilitylocation models: definition, formulation and solution approach. Annals of Operations Research, 6:49-74, 1986.
- 142. H. Tuy, A. Migdalas, and P. V~brand. A global optimization approach for the linear two-level program. Journal of Global Optimization, 3:1-23, 1993.
- 143. G. Onlti. A linear bilevel programming algorithm based on bicriteria programming. Computers and Operations Research, 14:173-179, 1987.
- 144. L. Vicente. Bilevel programming. Master's thesis, Department of Mathematics, University of Coimbra, 1992. Written in Portuguese.
- 145. L. Vicente and P. Calamai. Geometry and local optimality conditions for bilevel programs with quadratic strictly convex lower levels. Technical Report #198-O-150294, Department of Systems Design Engineering, University of Waterloo, 1994.
- 146. L. Vicente, G. Savard, and J. Jt~dice. Descent approaches for quadratic bilevel programming. Journal of Optimization Theoryand Applications, (forthcoming).
- 147. U. Wen. Mathematicalmethodsfor multilevel linearprogramming. PhD thesis, Department of Industrial Engineering, State University of New York at Buffalo, 1981.
- 148. U. Wen. The "Kth-Best" algorithm for multilevel programming. 1981. (Preprint from the
- 149. U.Wen. Asolutionprocedure fortheresourcecontrolproblemintwo-levelhierarchicaldecision processes. Journal of Chinese Institute of Engineers, 6:91-97, 1983.
- 150. U. Wen and W. Bialas. The hybrid algorithm for solving the three-level linear programming problem. Computersand OperationsResearch, 13:367-377, 1986.
- 151. U. Wen and S. Hsu. A note on a linear bilevel programming algorithm based on bicriteria programming. Computersand OperationsResearch, 16:79-83, 1989.
- 152. U. Wen and S. Hsu. Efficient solutions for the linear bilevel programming problem. European Journal of OperationalResearch, 62:354-362, 1991.
- 153. U. Wen and S. Hsu. Linear bi-level programming problems - a review. Journal of the OperationalResearch Society, 42:125-133, 1991.
- 154. U. Wen and Y. Yang. Algorithms for solving the mixed integer two-level linear programming problem. Computersand OperationsResearch, 17:133-142, 1990.
- 155. D. White and G. Anandalingam. A penalty function approach for solving hi-level linear programs. Journal of Global Optimization,3:397-419, 1993.
- 156. S. Wu, E Marcotte, and Y. Chen. A cutting plane method for linear bilevel programs. 1993. (Preprint from the Centre de Research sur les Transports).
- 157. J. Ye and D. Zhu. Optimality conditions for bilevel programming problems. Technical Report DMS-618-IR, Department of Mathematics and Statistics, University of Victoria, 1993. 1992, Revised 1993.
- 158. J. Ye, D. Zhu, and Q. Zhu. Generalized bilevel programming problems. Technical Report DMS-646-IR, Department of Mathematics and Statistics, University of Victoria, 1993.

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