Researchers working with nonlinear programming often claim "the word is non linear" indicating that real applications require nonlinear modeling. The same is true for other areas such as multi-objective programming (there are always several goals in a real application), stochastic programming (all data is uncer tain and therefore stochastic models should be used), and so forth. In this spirit we claim: The word is multilevel. In many decision processes there is a hierarchy of decision makers, and decisions are made at different levels in this hierarchy. One way to handle such hierar chies is to focus on one level and include other levels' behaviors as assumptions. Multilevel programming is the research area that focuses on the whole hierar chy structure. In terms of modeling, the constraint domain associated with a multilevel programming problem is implicitly determined by a series of opti mization problems which must be solved in a predetermined sequence. If only two levels are considered, we have one leader (associated with the upper level) and one follower (associated with the lower level).
Table of ContentsPreface. 1. Congested O-D Trip Demand Adjustment Problem: Bilevel Programming Formulation and Optimality Conditions; Yang Chen, M. Florian. 2. Determining Tax Credits for Converting Nonfood Crops to Biofuels: An Application of Bilevel Programming; J.F. Bard, et al. 3. Multilevel Optimization Methods in Mechanics; P.D. Panagiotopoulos, et al. 4. Optimal Structural Design in Nonsmooth Mechanics; G.E. Stavroulakis, H. Günzel. 5. Optimizing the Operations of an Aluminium Smelter Using Non-Linear Bi-Level Programming; M.G. Nicholls. 6. Complexity Issues in Bilevel Linear Programming; Xiaotie Deng. 7. The Computational Complexity of Multi-Level Bottleneck Programming Problems; T. Dudás, et al. 8. On the Linear Maxmin and Related Programming Problems; C. Audet, et al. 9. Piecewise Sequential Quadratic Programming for Mathematical Programs with Nonlinear Complementarity Constraints; Zhi-Quan Luo, et al. 10. A New Branch and Bound Method for Bilevel Linear Programs; Hoang Tuy, S. Ghannadan. 11. A Penalty Method for Linear Bilevel Programming Problems; M.A. Amouzegar, K. Moshirvaziri. 12. An Implicit Function Approach to Bilevel Programming Problems; S. Dempe. 13. Bilevel Linear Programming, Multiobjective Programming, and Monotonic Reverse Convex Programming; Hoang Tuy. 14. Existence of Solutions to Generalized Bilevel Programming Problem; M.B. Lignola, J. Morgan. 15. Application of Topological Degree Theory to Complementarity Problems; V.A. Bulavsky, et al. 16. Optimality and Dualityin Parametric Convex Lexicographic Programming; C.A. Floudas, S. Zlobec. Index.