Multilevel Optimization: Algorithms and Applications

1. Front Matter

   Pages i-xxii

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2. Congested O-D Trip Demand Adjustment Problem: Bilevel Programming Formulation and Optimality Conditions

   • Yang Chen, Michael Florian

   Pages 1-22

3. Determining Tax Credits for Converting Nonfood Crops to Biofuels: An Application of Bilevel Programming

   • Jonathan F. Bard, John Plummer, Jean Claude Sourie

   Pages 23-50

4. Multilevel Optimization Methods in Mechanics

   • P. D. Panagiotopoulos, E. S. Mistakidis, G. E. Stavroulakis, O. K. Panagouli

   Pages 51-90

5. Optimal Structural Design in Nonsmooth Mechanics

   • Georgios E. Stavroulakis, Harald Günzel

   Pages 91-115

6. Optimizing the Operations of an Aluminium Smelter Using Non-Linear Bi-Level Programming

   • Miles G. Nicholls

   Pages 117-148

7. Complexity Issues in Bilevel Linear Programming

   • Xiaotie Deng

   Pages 149-164

8. The Computational Complexity of Multi-Level Bottleneck Programming Problems

   • Tibor Dudás, Bettina Klinz, Gerhard J. Woeginger

   Pages 165-179

9. On the Linear Maxmin and Related Programming Problems

   • Charles Audet, Pierre Hansen, Brigitte Jaumard, Gilles Savard

   Pages 181-208

10. Piecewise Sequential Quadratic Programming for Mathematical Programs with Nonlinear Complementarity Constraints

    • Zhi-Quan Luo, Jong-Shi Pang, Daniel Ralph

    Pages 209-229

11. A New Branch and Bound Method for Bilevel Linear Programs

    • Hoang Tuy, Saied Ghannadan

    Pages 231-249

12. A Penalty Method for Linear Bilevel Programming Problems

    • Mahyar Amouzegar, Khosrow Moshirvaziri

    Pages 251-271

13. An Implicit Function Approach to Bilevel Programming Problems

    • Stephan Dempe

    Pages 273-294

14. Bilevel Linear Programming, Multiobjective Programming, and Monotonic Reverse Convex Programming

    • Hoang Thy

    Pages 295-314

15. Existence of Solutions to Generalized Bilevel Programming Problem

    • Maria Beatrice Lignola, Jacqueline Morgan

    Pages 315-332

16. Application of Topological Degree Theory to Complementarity Problems

    • Vladimir A. Bulavsky, George Isac, Vyacheslav V. Kalashnikov

    Pages 333-358

17. Optimality and Duality in Parametric Convex Lexicographic Programming

    • C. A. Floudas, S. Zlobec

    Pages 359-379

18. Back Matter

    Pages 381-386

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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).

• algorithms
• complexity
• computation
• computational complexity
• design
• linear optimization
• Mathematica
• mechanics
• modeling
• nonlinear optimization
• optimization
• programming
• quadratic programming

• Division of Optimization, Department of Mathematics, Linköping Institute of Technology, Linköping, Sweden

  Athanasios Migdalas, Peter Värbrand

• Department of Industrial and Systems Engineering, University of Florida, Gainesville, USA

  Panos M. Pardalos

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