Skip to main content
Springer Nature Link
Log in

Editorial: Hierarchical and bilevel programming

  • Published:
Journal of Global Optimization Aims and scope Submit manuscript

Abstract

Approximately twenty years ago the modern interest for hierarchical programming was initiated by J. Bracken and J.M. McGill [9], [10]. The activities in the field have ever grown lively, both in terms of theoretical developments and terms of the diversity of the applications. The collection of seven papers in this issue covers a diverse number of topics and provides a good picture of recent research activities in the field of bilevel and hierarchical programming. The papers can be roughly divided into three categories; Linear bilevel programming is addressed in the first two papers by Gendreau et al and Moshirvaziri et al; The following three papers by Nicholls, Loridan & Morgan, and Kalashnikov & Kalashnikova are concerned with nonlinear bilevel programming; and, finally, Wen & Lin and Nagase & Aiyoshi address hierarchical decision making issues relating to both biobjective and bilevel programming.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. J.P. Aubin (1979) Mathematical Methods of Game and Economic Theory, North-Holland, Amsterdam

    Google Scholar 

  2. G. Anandalingam and T.L. Friesz (eds.) (1992), Hierarchical Optimization, Annals of Operations Research 34, J.C. Baltzer AG, Basel, Switzerland

    Google Scholar 

  3. J.F. Bard (1983) An Efficient Point Algorithm for a Linear Two-Stage Optimization Problem, Operations Research 31, 670–684

    Google Scholar 

  4. J.F. Bard (1991) Some Properties of the Bilevel Programming Problem, Journal of Optimization Theory and Application 68, 371–378

    Google Scholar 

  5. T. Başar and G.J. Olsder (1982) Dynamic Noncooperative Game Theory, Academic Press, London

    Google Scholar 

  6. O. Ben-Ayed and C.E. Blair (1990) Computational Difficulties of Bilevel Linear Programming, Operations Research 38, 556–560

    Google Scholar 

  7. H.P. Benson (1984) Optimization over Efficient Set, Journal of Mathematical Analysis and Applications 98, 562–580

    Google Scholar 

  8. C. Blair (1992) The Computational Complexity of Multi-Level Linear Programs, in: [2], 13–19

  9. J. Bracken and J.M. McGill (1973), Mathematical Programs with Optimization Problems in the Constraints, Operations Research 21, 37–44

    Google Scholar 

  10. J. Bracken and J.M. McGill (1974), A Method for Solving Mathematical Programs with Nonlinear Programs in the Constraints, Operations Research 22, 1097–1101

    Google Scholar 

  11. T.L. Friesz, R.L. Tobin, H.J. Cho and N.J. Mehta (1990) Sensitivity Analysis Based Heuristic Algorithms for Mathematical Programs with Variational Inequality Constraints, Mathematical Programming 48, 265–284

    Google Scholar 

  12. P. Hansen, B. Jaumard and G. Savard (1992) New Branch-and-Bound Rules for Linear Bilevel Programming, SIAM Journal on Scientific and Statistical Computing 13, 1194–1217

    Google Scholar 

  13. P.T. Harker and J.S. Pang (1990) Finite Dimensional Variational Inequality and Nonlinear Complementarity Problems: A Survey of Theory, Algorithms and Applications, Mathematical Programming 48, 161–220

    Google Scholar 

  14. R.G. Jeroslow (1985) The Polynomial Hierarchy and Simple Model for Competitive Analysis, Mathematical Programming 32, pp. 131–153

    Google Scholar 

  15. L. J. LeBlanc and D.E. Boyce (1986) A Bilevel Programming Algorithm for Exact Solution of the Network Design Problem with User Optimal Flows, Transportations Research 20B, 259–265

    Google Scholar 

  16. M.B. Lignola and J. Morgan (1993) Regularized Bilevel Programming Problem, Preprint n. 22/93, Dip. di Matematica e Applicazioni“ R. Coccioppoli”, Universita degli Studi di Napoli “Federico II”, Napoli, Italy

  17. L. Mallozzi and J. Morgan (1995) Weak Stackelberg Problem and Mixed Solutions under Data Perturbations, Optimization 32, 269–290

    Google Scholar 

  18. P. Marcotte (1986) Network Design Problem with Congestion Effects: A Case of Bilevel Programming, Mathematical Programming 34, 142–162

    Google Scholar 

  19. P. Marcotte (1988) A Note on the Bilevel Programming Algorithm by LeBlanc and Boyce, Transportation Research 22B, 233–237

    Google Scholar 

  20. A. Migdalas (1995) Bilevel Programming in Traffic Planning: Models Methods and Challenge, Journal of Global Optimization 7, 381–405

    Google Scholar 

  21. A. Migdalas (1995) When is a Stackelberg Equilibrium Pareto Optimum?, in: Advances in Multicriteria Analysis, P.M. Pardalos, Y. Siskos and C. Zopounidis (eds.), Kluwer Academic Publishers, Dordrecht, 175–181

    Google Scholar 

  22. D.A. Molodsov (1976) The Solution of a Class of Non Antagonistic Games, USSR Comput. Math. i Math. Phys. 16, 1451–1456

    Google Scholar 

  23. S.C. Narula and A.D. Nwosu (1991) Two-Level Resource Control Pre-Emptive Hierarchical Linear Programming Problem: A Review, in: Recent Development in Mathematical Programming, S. Kumar (ed.), Gordon and Breach Science Publishers, Philadelphia, 29–43

    Google Scholar 

  24. J.V. Outrata (1994) On Optimization Problems with Variational Inequality Constraints, SIAM J. Optimization 4, 340–357

    Google Scholar 

  25. H. von Stackelberg (1952) The Theory of the Market Economy, Oxford University Press.

  26. L.N. Vicente and P.H. Calamai (1994) Bilevel and Multilevel programming: A Bibliography Review, Journal of Global Optimization 5, 291–306

    Google Scholar 

  27. L.N. Vicente and P.H. Calamai (1995) Geometry and Local Optimality Conditions for Bilevel Programs with Quadratic Strictly Convex Lower Levels, in: Minimax and Applications, D.-Z. Du and P.M. Pardalos (eds.), Kluwer Academic Publishers, Dordrecht, 141–151

    Google Scholar 

  28. G. Ünlü (1987) A Linear Bilevel Programming Algorithm Based on Bicreteria Programming, Computers and Operations Research 14, 173–179

    Google Scholar 

  29. U.-P. Wen and S.-T. Hsu (1989) A Note on a Linear Bilevel Programming Algorithm Based on Bicreteria Programming, Computers and Operations Research 16, 79–83

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Division of Optimization, Department of Mathematics, Linköping Institute of Technology, S-581 83, Linköping, Sweden

    Athanasios Migdalas

  2. Center for Applied Optimization, University of Florida, 32611-6595, Gainesville, FL, USA

    Panos M. Pardalos

  3. Department of Industrial and Systems Engineering, University of Florida, 32611-6595, Gainesville, FL, USA

    Panos M. Pardalos

Authors
  1. Athanasios Migdalas
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Panos M. Pardalos
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Migdalas, A., Pardalos, P.M. Editorial: Hierarchical and bilevel programming. J Glob Optim 8, 209–215 (1996). https://doi.org/10.1007/BF00121265

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00121265

Keywords