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Team optimization problems with Lipschitz continuous strategies. (English) Zbl 1242.90144

Summary: 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.

MSC:

90C15 Stochastic programming
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[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) · Zbl 0436.90004 · doi:10.1016/0096-3003(80)90013-2
[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) · Zbl 1151.93029 · doi:10.1109/TNN.2006.883015
[3] Alessandri A., Cervellera C., Sanguineti M.: Functional optimal estimation problems and their approximate solution. J. Optim. Theory Appl. 134, 445–466 (2007) · Zbl 1151.93029 · doi:10.1007/s10957-007-9229-6
[4] Arrow K.J.: Individual Choice Under Certainty and Uncertainty. Belknap Press, Cambridge (1984)
[5] Berkovitz L.D.: Convexity and Optimization in $${{\(\backslash\)mathbb R}\^n}$$ . Wiley, New York (2002) · Zbl 0991.90002
[6] Clarke F.H.: Optimization and Nonsmooth Analysis. Wiley, New York (1983) · Zbl 0582.49001
[7] Dudley R.M.: Real Analysis and Probability. Cambridge University Press, Cambridge (2002) · Zbl 1023.60001
[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) · Zbl 1179.90325
[9] Gnecco, G., Sanguineti, M.: Suboptimal solutions to network team optimization problems. In: CD-Proceedings of International Network Optimization Conference (INOC), Pisa, Italy (2009) · Zbl 1179.90325
[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) · Zbl 1274.91136
[11] Haykin S.: Neural Networks. A Comprehensive Foundation. Prentice-Hall, Englewood Cliffs (1999) · Zbl 0934.68076
[12] Hess J., Ider Z., Kagiwada H., Kalaba R.: Team decision theory and integral equations. J. Optim. Theory Appl. 22, 251–264 (1977) · Zbl 0353.90109 · doi:10.1007/BF00933166
[13] Hiriart-Urruty J.B., Lemaréchal C.: Convex Analysis and Minimization Algorithms I. Springer, Berlin (1993) · Zbl 0795.49001
[14] Kim K.H., Roush F.W.: Team Theory. Ellis Horwood Limited, Chichester (1987) · Zbl 0643.90001
[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) · doi:10.2307/2582195
[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) · Zbl 0493.93056 · doi:10.1109/TAC.1982.1103007
[17] Maroto J.M., Moran M.: Lipschitz continuous dynamic programming with discount II. Nonlinear Anal. 67, 1999–2011 (2007) · Zbl 1149.90170 · doi:10.1016/j.na.2006.08.027
[18] Marschak J., Radner R.: Economic Theory of Teams. Yale University Press, New Haven (1972) · Zbl 0252.90003
[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) · doi:10.1137/1030165
[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) · Zbl 1151.90546
[21] Rockafellar R.T., Wets R.J.B.: Variational Analysis. Springer, Berlin (2004)
[22] Rudin W.: Real and Complex Analysis. McGraw-Hill, Singapore (1987) · Zbl 0925.00005
[23] Rudin W.: Principles of Mathematical Analysis, III Edition. McGraw-Hill, Singapore (1976) · Zbl 0346.26002
[24] Witsenhausen H.S.: Equivalent stochastic control problems. Math. Control Signals Syst. 1, 3–11 (1988) · Zbl 0659.93078 · doi:10.1007/BF02551232
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