×

zbMATH — the first resource for mathematics

Existence and global asymptotic stability of optimal trajectories for a class of infinite-horizon, nonconvex systems. (English) Zbl 0417.49023

MSC:
49K15 Optimality conditions for problems involving ordinary differential equations
49K40 Sensitivity, stability, well-posedness
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Samuelson, P. A., andSolow, R. H.,A Complete Capital Model Involving Heterogeneous Capital Goods, Quarterly Journal of Economics, Vol. 70, pp. 537-562, 1956. · doi:10.2307/1881864
[2] Radner, R.,Paths of Economic Growth That Are Optimal with Regard Only to Final States, Review of Economic Studies, Vol. 28, pp. 98-104, 1961. · doi:10.2307/2295707
[3] McKenzie, L. W.,Accumulation Programs of Maximum Utility and the Von Neumann Facet, Value Capital and Growth, Edited by J. N. Wolfe, University Press, Edinburgh, Scotland, 1968.
[4] Gale, D.,On Optimal Development in a Multi-Sector Economy, Review of Economic Studies, Vol. 34, pp. 1-18, 1967. · doi:10.2307/2296567
[5] Brock, W. A.,On the Existence of Weakly Maximal Programmes in a Multi-Sector Economy, Review of Economic Studies, Vol. 37, pp. 275-280, 1970. · Zbl 0212.23901 · doi:10.2307/2296419
[6] Rockafellar, T.,Saddle Points of Hamiltonian Systems in Convex Problems of Lagrange, Journal of Optimization Theory and Applications, Vol. 12, pp. 367-390, 1973. · Zbl 0263.49022 · doi:10.1007/BF00940418
[7] Haurie, A.,Optimal Control of an Infinite-Time Horizon, Journal of Mathematical Economics, Vol. 3, pp. 81-102, 1976. · Zbl 0329.90021 · doi:10.1016/0304-4068(76)90007-0
[8] Brock, W. A., andHaurie, A.,On Existence of Overtaking Optimal Trajectories over an Infinite-Time Horizon, Mathematics of Operations Research, Vol. 1, pp. 337-346, 1976. · Zbl 0367.49003 · doi:10.1287/moor.1.4.337
[9] Cass, D., andShell, K.,The Structure and Stability of Competitive Dynamical Systems, Journal of Economic Theory, Vol. 12, pp. 31-70, 1976. · Zbl 0348.90039 · doi:10.1016/0022-0531(76)90027-2
[10] Rockafellar, T.,Saddle Points of Hamiltonian Systems in Convex Lagrange Problems Having a Nonzero Discount Rate, Journal of Economic Theory, Vol. 12, pp. 71-113, 1976. · Zbl 0333.90007 · doi:10.1016/0022-0531(76)90028-4
[11] Brock, W. A., andScheinkman, J.,Global Asymptotic Stability of Optimal Control Systems, with Applications to the Theory of Economic Growth, Journal of Economic Theory, Vol. 12, pp. 164-190, 1976. · Zbl 0348.90018 · doi:10.1016/0022-0531(76)90031-4
[12] Haurie, A., andHung, N. M.,Further Aspects of Turnpike Theory in Continuous Time with Applications, Journal of Dynamic Systems, Measurement, and Control, Vol. 98, pp. 85-90, 1976. · Zbl 0333.90009 · doi:10.1115/1.3426992
[13] McKenzie, L. W.,Turnpike Theory, Econometrica, Vol. 44, pp. 841-866, 1976. · Zbl 0356.90006 · doi:10.2307/1911532
[14] Varaiya, P.,On the Trajectories of a Differential System, Mathematical Theory of Control, Edited by A. V. Balakrishnan and L. Neustadt, Academic Press, New York, New York, 1967. · Zbl 0235.49009
[15] Baum, R. F.,Existence Theorems for Lagrange Control Problems with Unbounded Time Domain, Journal of Optimization Theory and Applications, Vol. 19, pp. 89-116, 1976. · Zbl 0305.49002 · doi:10.1007/BF00934054
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.