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Stability of a turnpike phenomenon for a class of optimal control systems in metric spaces
1. | Department of Mathematics, Technion-Israel Institute of Technology, Haifa, 32000, Israel |
References:
[1] |
S. Aubry and P. Y. Le Daeron, The discrete Frenkel-Kontorova model and its extensions I , Physica D, 8 (1983), 381-422.
doi: doi:10.1016/0167-2789(83)90233-6. |
[2] |
J. Blot, Infinite-horizon Pontryagin principles without invertibility, J. Nonlinear Convex Anal., 10 (2009), 177-189. |
[3] |
J. Blot and P. Cartigny, Optimality in infinite-horizon variational problems under sign conditions, J. Optim. Theory Appl., 106 (2000), 411-419.
doi: doi:10.1023/A:1004611816252. |
[4] |
P. Cartigny and P. Michel, On a sufficient transversality condition for infinite horizon optimal control problems, Automatica J. IFAC, 39 (2003), 1007-1010.
doi: doi:10.1016/S0005-1098(03)00060-8. |
[5] |
D. Gale, On optimal development in a multi-sector economy, Review of Economic Studies, 34 (1967), 1-18.
doi: doi:10.2307/2296567. |
[6] |
A. Leizarowitz, Infinite horizon autonomous systems with unbounded cost, Appl. Math. and Opt., 13 (1985), 19-43.
doi: doi:10.1007/BF01442197. |
[7] |
A. Leizarowitz, Tracking nonperiodic trajectories with the overtaking criterion, Appl. Math. and Opt., 14 (1986), 155-171.
doi: doi:10.1007/BF01442233. |
[8] |
A. Leizarowitz and V. J. Mizel, One dimensional infinite horizon variational problems arising in continuum mechanics, Arch. Rational Mech. Anal., 106 (1989), 161-194.
doi: doi:10.1007/BF00251430. |
[9] |
V. Lykina, S. Pickenhain and M. Wagner, Different interpretations of the improper integral objective in an infinite horizon control problem, J. Math. Anal. Appl, 340 (2008), 498-510.
doi: doi:10.1016/j.jmaa.2007.08.008. |
[10] |
V. L. Makarov and A. M. Rubinov, "Mathematical Theory of Economic Dynamics and Equilibria,'' Springer-Verlag, New York, 1977. |
[11] |
M. A. Mamedov and S. Pehlivan, Statistical convergence of optimal paths, Math. Japon., 52 (2000), 51-55. |
[12] |
M. A. Mamedov and S. Pehlivan, Statistical cluster points and turnpike theorem in nonconvex problems, J. Math. Anal. Appl., 256 (2001), 686-693.
doi: doi:10.1006/jmaa.2000.7061. |
[13] |
L. W. McKenzie, Turnpike theory, Econometrica 44 (1976), 841-866.
doi: doi:10.2307/1911532. |
[14] |
B. Mordukhovich, Minimax design for a class of distributed parameter systems, Automat. Remote Control, 50 (1990), 1333-1340. |
[15] |
B. Mordukhovich and I. Shvartsman, Optimization and feedback control of constrained parabolic systems under uncertain perturbations, in "Optimal Control, Stabilization and Nonsmooth Analysis,'' Lecture Notes Control Inform. Sci. Springer, 2004, 121-132. |
[16] |
J. Moser, Minimal solutions of variational problems on a torus, Ann. Inst. H. Poincare, Analyse Nonlineare, 3 (1986), 229-272. |
[17] |
S. Pickenhain, V. Lykina and M. Wagner, On the lower semicontinuity of functionals involving Lebesgue or improper Riemann integrals in infinite horizon optimal control problems, Control Cybernet. 37 (2008), 451-468. |
[18] |
A. M. Rubinov, Economic dynamics, J. Soviet Math., 26 (1984), 1975-2012.
doi: doi:10.1007/BF01084444. |
[19] |
P. A. Samuelson, A catenary turnpike theorem involving consumption and the golden rule, American Economic Review, 55 (1965), 486-496. |
[20] |
A. J. Zaslavski, Optimal programs on infinite horizon 1, SIAM Journal on Control and Optimization, 33 (1995), 1643-1660.
doi: doi:10.1137/S036301299325726X. |
[21] |
A. J. Zaslavski, Optimal programs on infinite horizon 2, SIAM Journal on Control and Optimization, 33 (1995), 1661-1686.
doi: doi:10.1137/S0363012993257271. |
[22] |
A. J. Zaslavski, "Turnpike Properties in the Calculus of Variations and Optimal Control,'' Springer, New York, 2006. |
[23] |
A. J. Zaslavski, Turnpike results for a discrete-time optimal control system arising in economic dynamics, Nonlinear Analysis, 67 (2007), 2024-2049.
doi: doi:10.1016/j.na.2006.08.029. |
[24] |
A. J. Zaslavski, Two turnpike results for a discrete-time optimal control system, Nonlinear Analysis, 71 (2009), 902-909.
doi: doi:10.1016/j.na.2008.12.053. |
[25] |
A. J .Zaslavski, Stability of a turnpike phenomenon for a discrete-time optimal control system, J. Optim. Theory Appl., 145 (2010), 597-612.
doi: doi:10.1007/s10957-010-9677-2. |
show all references
References:
[1] |
S. Aubry and P. Y. Le Daeron, The discrete Frenkel-Kontorova model and its extensions I , Physica D, 8 (1983), 381-422.
doi: doi:10.1016/0167-2789(83)90233-6. |
[2] |
J. Blot, Infinite-horizon Pontryagin principles without invertibility, J. Nonlinear Convex Anal., 10 (2009), 177-189. |
[3] |
J. Blot and P. Cartigny, Optimality in infinite-horizon variational problems under sign conditions, J. Optim. Theory Appl., 106 (2000), 411-419.
doi: doi:10.1023/A:1004611816252. |
[4] |
P. Cartigny and P. Michel, On a sufficient transversality condition for infinite horizon optimal control problems, Automatica J. IFAC, 39 (2003), 1007-1010.
doi: doi:10.1016/S0005-1098(03)00060-8. |
[5] |
D. Gale, On optimal development in a multi-sector economy, Review of Economic Studies, 34 (1967), 1-18.
doi: doi:10.2307/2296567. |
[6] |
A. Leizarowitz, Infinite horizon autonomous systems with unbounded cost, Appl. Math. and Opt., 13 (1985), 19-43.
doi: doi:10.1007/BF01442197. |
[7] |
A. Leizarowitz, Tracking nonperiodic trajectories with the overtaking criterion, Appl. Math. and Opt., 14 (1986), 155-171.
doi: doi:10.1007/BF01442233. |
[8] |
A. Leizarowitz and V. J. Mizel, One dimensional infinite horizon variational problems arising in continuum mechanics, Arch. Rational Mech. Anal., 106 (1989), 161-194.
doi: doi:10.1007/BF00251430. |
[9] |
V. Lykina, S. Pickenhain and M. Wagner, Different interpretations of the improper integral objective in an infinite horizon control problem, J. Math. Anal. Appl, 340 (2008), 498-510.
doi: doi:10.1016/j.jmaa.2007.08.008. |
[10] |
V. L. Makarov and A. M. Rubinov, "Mathematical Theory of Economic Dynamics and Equilibria,'' Springer-Verlag, New York, 1977. |
[11] |
M. A. Mamedov and S. Pehlivan, Statistical convergence of optimal paths, Math. Japon., 52 (2000), 51-55. |
[12] |
M. A. Mamedov and S. Pehlivan, Statistical cluster points and turnpike theorem in nonconvex problems, J. Math. Anal. Appl., 256 (2001), 686-693.
doi: doi:10.1006/jmaa.2000.7061. |
[13] |
L. W. McKenzie, Turnpike theory, Econometrica 44 (1976), 841-866.
doi: doi:10.2307/1911532. |
[14] |
B. Mordukhovich, Minimax design for a class of distributed parameter systems, Automat. Remote Control, 50 (1990), 1333-1340. |
[15] |
B. Mordukhovich and I. Shvartsman, Optimization and feedback control of constrained parabolic systems under uncertain perturbations, in "Optimal Control, Stabilization and Nonsmooth Analysis,'' Lecture Notes Control Inform. Sci. Springer, 2004, 121-132. |
[16] |
J. Moser, Minimal solutions of variational problems on a torus, Ann. Inst. H. Poincare, Analyse Nonlineare, 3 (1986), 229-272. |
[17] |
S. Pickenhain, V. Lykina and M. Wagner, On the lower semicontinuity of functionals involving Lebesgue or improper Riemann integrals in infinite horizon optimal control problems, Control Cybernet. 37 (2008), 451-468. |
[18] |
A. M. Rubinov, Economic dynamics, J. Soviet Math., 26 (1984), 1975-2012.
doi: doi:10.1007/BF01084444. |
[19] |
P. A. Samuelson, A catenary turnpike theorem involving consumption and the golden rule, American Economic Review, 55 (1965), 486-496. |
[20] |
A. J. Zaslavski, Optimal programs on infinite horizon 1, SIAM Journal on Control and Optimization, 33 (1995), 1643-1660.
doi: doi:10.1137/S036301299325726X. |
[21] |
A. J. Zaslavski, Optimal programs on infinite horizon 2, SIAM Journal on Control and Optimization, 33 (1995), 1661-1686.
doi: doi:10.1137/S0363012993257271. |
[22] |
A. J. Zaslavski, "Turnpike Properties in the Calculus of Variations and Optimal Control,'' Springer, New York, 2006. |
[23] |
A. J. Zaslavski, Turnpike results for a discrete-time optimal control system arising in economic dynamics, Nonlinear Analysis, 67 (2007), 2024-2049.
doi: doi:10.1016/j.na.2006.08.029. |
[24] |
A. J. Zaslavski, Two turnpike results for a discrete-time optimal control system, Nonlinear Analysis, 71 (2009), 902-909.
doi: doi:10.1016/j.na.2008.12.053. |
[25] |
A. J .Zaslavski, Stability of a turnpike phenomenon for a discrete-time optimal control system, J. Optim. Theory Appl., 145 (2010), 597-612.
doi: doi:10.1007/s10957-010-9677-2. |
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