Multilevel Optimization: Algorithms and Applications

ISBN-13: 9781461379898 / Angielski / Miękka / 2011 / 386 str.

A. Migdalas; Panos M. Pardalos; Peter V. Rbrand

Opis

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).

Spis treści

Preface. 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.