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Multilevel Optimization: Algorithms and Applications

  • Book
  • © 1998

Overview

Editors:
  1. Athanasios Migdalas

    1. Division of Optimization, Department of Mathematics, Linköping Institute of Technology, Linköping, Sweden

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  2. Panos M. Pardalos

    1. Department of Industrial and Systems Engineering, University of Florida, Gainesville, USA

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  3. Peter Värbrand

    1. Division of Optimization, Department of Mathematics, Linköping Institute of Technology, Linköping, Sweden

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Part of the book series: Nonconvex Optimization and Its Applications (NOIA, volume 20)

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Table of contents (16 chapters)

  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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Keywords

About this book

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).

Editors and Affiliations

  • 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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