Skip to main content
Log in

Team optimization problems with Lipschitz continuous strategies

  • Original Paper
  • Published:
Optimization Letters Aims and scope Submit manuscript

Abstract

Sufficient conditions for the existence and Lipschitz continuity of optimal strategies for static team optimization problems are studied. Revised statements and proofs of some results appeared in the literature are presented. Their extensions are discussed. As an example of application, optimal production in a multidivisional firm is considered.

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

Access this article

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.

Similar content being viewed by others

References

  1. Akbari A., Hess J., Kagiwada H., Kalaba R.: The equivalence of team theory’s integral equations and a Cauchy system: sensitivity analysis of a variational problem. Appl. Math. Comput. 6, 21–36 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  2. Alessandri A., Cervellera C., Sanguineti M.: Design of asymptotic estimators: an approach based on neural networks and nonlinear programming. IEEE Trans. Neural Netw. 18, 86–96 (2007)

    Article  Google Scholar 

  3. Alessandri A., Cervellera C., Sanguineti M.: Functional optimal estimation problems and their approximate solution. J. Optim. Theory Appl. 134, 445–466 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  4. Arrow K.J.: Individual Choice Under Certainty and Uncertainty. Belknap Press, Cambridge (1984)

    Google Scholar 

  5. Berkovitz L.D.: Convexity and Optimization in \({{\mathbb R}^n}\) . Wiley, New York (2002)

    Book  MATH  Google Scholar 

  6. Clarke F.H.: Optimization and Nonsmooth Analysis. Wiley, New York (1983)

    MATH  Google Scholar 

  7. Dudley R.M.: Real Analysis and Probability. Cambridge University Press, Cambridge (2002)

    Book  MATH  Google Scholar 

  8. Gnecco, G., Sanguineti, M.: Lipschitz continuity of the solutions to team optimization problems revisited. In: Proceedings of International Conference on Mathematical Science and Engineering, Venice, Italy (2009)

  9. Gnecco, G., Sanguineti, M.: Suboptimal solutions to network team optimization problems. In: CD-Proceedings of International Network Optimization Conference (INOC), Pisa, Italy (2009)

  10. Gnecco, G., Sanguineti, M.: Smooth optimal decision strategies for static team optimization problems and their approximations. In: Lecture Notes in Computer Science. Proceedings of 36th International Conference SOFSEM 2010, vol. 5901, pp. 440–451. Springer, Heidelberg (2010)

  11. Haykin S.: Neural Networks. A Comprehensive Foundation. Prentice-Hall, Englewood Cliffs (1999)

    MATH  Google Scholar 

  12. Hess J., Ider Z., Kagiwada H., Kalaba R.: Team decision theory and integral equations. J. Optim. Theory Appl. 22, 251–264 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  13. Hiriart-Urruty J.B., Lemaréchal C.: Convex Analysis and Minimization Algorithms I. Springer, Berlin (1993)

    Google Scholar 

  14. Kim K.H., Roush F.W.: Team Theory. Ellis Horwood Limited, Chichester (1987)

    MATH  Google Scholar 

  15. Klein J.H.: Review of ‘Team Theory, by K. H. Kim and F. W. Roush, Ellis Horwood Limited, Chichester, 1987’. J. Oper. Res. Soc. 39, 695–696 (1988)

    Article  Google Scholar 

  16. Krainak J.C., Speyer J.L., Marcus S.I.: Static team problems—Part I: sufficient conditions and the exponential cost criterion. IEEE Trans. Authom. Control 27, 839–848 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  17. Maroto J.M., Moran M.: Lipschitz continuous dynamic programming with discount II. Nonlinear Anal. 67, 1999–2011 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  18. Marschak J., Radner R.: Economic Theory of Teams. Yale University Press, New Haven (1972)

    MATH  Google Scholar 

  19. Packel E.W.: Review of ‘Team Theory, by K. H. Kim and F. W. Roush, Ellis Horwood Limited, Chichester, 1987’. SIAM Rev 30, 676–677 (1988)

    Article  MathSciNet  Google Scholar 

  20. Pappalardo M.: Multiobjective optimization: a brief overview. In: Chinchuluun, A., Pardalos, P., Migdalas, A., Pitsoulis, L. (eds) Pareto Optimality, Game Theory and Equilibria, Springer Series Optimization and Its Applications, vol. 17, pp. 517–528. Springer, New York (2008)

    Chapter  Google Scholar 

  21. Rockafellar R.T., Wets R.J.B.: Variational Analysis. Springer, Berlin (2004)

    Google Scholar 

  22. Rudin W.: Real and Complex Analysis. McGraw-Hill, Singapore (1987)

    MATH  Google Scholar 

  23. Rudin W.: Principles of Mathematical Analysis, III Edition. McGraw-Hill, Singapore (1976)

    Google Scholar 

  24. Witsenhausen H.S.: Equivalent stochastic control problems. Math. Control Signals Syst. 1, 3–11 (1988)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Marcello Sanguineti.

Additional information

The authors were partially supported by a grant “Progetti di Ricerca di Ateneo 2008” of the University of Genoa, project “Solution of Functional Optimization Problems by Nonlinear Approximators and Learning from Data”.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gnecco, G., Sanguineti, M. Team optimization problems with Lipschitz continuous strategies. Optim Lett 5, 333–346 (2011). https://doi.org/10.1007/s11590-010-0213-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11590-010-0213-y

Keywords

Navigation