×

zbMATH — the first resource for mathematics

Sufficient optimality conditions for nonconvex control problems with state constraints. (English) Zbl 0651.49009
The sufficient optimality conditions of V. Zeidan [Appl. Math. Optimization 11, 209-226 (1984; Zbl 0558.49006); and Trans. Am. Math. Soc. 275, 561-586 (1983; Zbl 0513.49010)] for optimal control problems are generalized such that they are applicable to problems with pure state-variable inequality constraints. We derive conditions which do neither assume the concavity of the Hamiltonian nor the quasiconcavity of the constraints. Global as well as local optimality conditions are presented.
Reviewer: G.Sorger

MSC:
49K15 Optimality conditions for problems involving ordinary differential equations
49L99 Hamilton-Jacobi theories
93C15 Control/observation systems governed by ordinary differential equations
34H05 Control problems involving ordinary differential equations
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Zeidan, V.,First and Second Order Sufficient Conditions for Optimal Control and the Calculus of Variations, Applied Mathematics and Optimization, Vol. 11, pp. 209-226, 1984. · Zbl 0558.49006 · doi:10.1007/BF01442179
[2] Zeidan, V.,Sufficient Conditions for the Generalized Problem of Bolza, Transactions of the American Mathematical Society, Vol. 275, pp. 561-586, 1983. · Zbl 0513.49010 · doi:10.1090/S0002-9947-1983-0682718-3
[3] Zeidan, V.,A Modified Hamilton-Jacobi Approach in the Generalized Problem of Bolza, Applied Mathematics and Optimization, Vol. 11, pp. 97-109, 1984. · Zbl 0558.49005 · doi:10.1007/BF01442172
[4] Zeidan, V.,Sufficient Conditions for Optimal Control and the Generalized Problem of Bolza, PhD Thesis, University of British Columbia, Vancouver, Canada, 1982.
[5] Mangasarian, O. L.,Sufficient Conditions for the Optimal Control of Nonlinear Systems, SIAM Journal on Control and Optimization, Vol. 4, pp. 139-152, 1966. · Zbl 0154.10401 · doi:10.1137/0304013
[6] Arrow, K. J.,Applications of Control Theory to Economic Growth, Mathematics of the Decision Sciences, Edited by G. B. Dantzig and A. F. Veinott, American Mathematical Society, Providence, Rhode Island, pp. 85-119, 1968.
[7] Seierstad, A., andSydsaeter, K.,Sufficient Conditions in Optimal Control Theory, International Economic Review, Vol. 18, pp. 367-391, 1977. · Zbl 0392.49010 · doi:10.2307/2525753
[8] Leitmann, G., andStalford, H.,A Sufficiency Theorem for Optimal Control, Journal of Optimization Theory and Applications, Vol. 8, pp. 169-174, 1971. · Zbl 0219.49005 · doi:10.1007/BF00932465
[9] Clarke, F. H.,Optimization and Nonsmooth Analysis, Wiley, New York, New York, 1983. · Zbl 0582.49001
[10] Fleming, W. H.,Functions of Several Variables, Springer, New York, New York, 1977. · Zbl 0348.26002
[11] Blagodatskikh, V. I.,Sufficient Conditions for Optimality in Problems with State Constraints, Applied Mathematics and Optimization, Vol. 7, pp. 149-157, 1981. · Zbl 0485.49013 · doi:10.1007/BF01442113
[12] Derzko, N. A., Sethi, S. P., andThompson, G. L.,Necessary and Sufficient Conditions for Optimal Control of Quasilinear Partial Differential Systems, Journal of Optimization Theory and Applications, Vol. 43, pp. 89-101, 1984. · Zbl 0518.49016 · doi:10.1007/BF00934748
[13] Hartl, R. F.,Arrow-Type Sufficient Optimality Conditions for Nondifferentiable Optimal Control Problems with State Constraints, Applied Mathematics and Optimization, Vol. 14, pp. 229-247, 1986. · Zbl 0614.49016 · doi:10.1007/BF01442238
[14] Seierstad, A., andSydsaeter, K.,Optimal Control Theory with Economic Applications, North-Holland, Amsterdam, Holland, 1987. · Zbl 0613.49001
[15] Reid, W. T.,Riccati Differential Equations, Academic Press, London, England, 1972. · Zbl 0254.34003
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.