Necessary optimality conditions for discrete systems with state-dependent control region

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1. M. Canon C. Cullum E. Polak, Constrained minimization problems in finite dimensional spaces, SIAM J. Control 4 (1966), 3, 528-547. (1966) MR0207423
2. N. O. DaCunha E. Polak, Constrained minimization under vector-valued criteria in finite dimensional spaces, J. Math. Anal. Applies. 19 (1967), 1, 103-124. (1967) MR0216346
3. M. D. Canon C. D. Cullum E. Polak, Theory of Optimal Control and Mathematical Programming, McGraw-Hill, New York 1970. (1970) MR0397497
4. A. Blaqiuère F. Gérard G. Leitman, Quantitative and Qualitative Games, Academic Press, New York 1969. (1969) MR0261973
5. B. Г. Болтянский, Оптимальное управление дискретным системами, Наука, Москва 1973. (1973) Zbl1170.01397
6. L. S. Pontrjagin V. G. Boltjanskij R. V. Gamkrelidze J. F. Miščenko, Matematická teorie optimálních procesů, SNTL, Praha 1964. (1964) 
7. M. R. Hestenes, Calculus of Variations and Optimal Control Theory, Wiley and Sons, New York 1966. (1966) Zbl0173.35703MR0203540
8. A. Я. Дубовицкий А. А. Милютин, Задачи на экстремум при надичии ограничений, Журнал выч. математики и мат. физики 5 (1965), 3, 395-453. (1965) Zbl1225.00032MR0191691
9. L. W. Neustadt, A general theory of extremals, J. Comp. Syst. Sci. 3 (1969), 1, 57-92. (1969) Zbl0167.08802MR0243405
10. P. B. Гамкрелидзе Г. Л. Харатишвили, Экстремальные задачи в линейных топологических пространствах, Изв. AH CCCP сер. мат. 33 (1969) 4, 781-839. (1969) Zbl1231.90028
11. R. V. Gamkrelidze, First-order necessary conditions and axiomatics for extremal problems, Proc. Steklov Inst. Math. 112 (1971), 156-186. (1971) MR0331169
12. J. Doležal, Problémy diskrétního optimálního řízení a diferenční hry, Thesis ÚTIA ČSAV, Praha 1973. (1973) 
13. J. Doležal, Existence of optimal solutions in general discrete systems, Kybernetika 11 (1975), 4, 301-312. (1975) MR0490220
14. J. M. Holtzman, Convexity and maximum principle for discrete systems, IEEE Trans. Autom. Contr. AC-11 (1966), 1, 30-35. (1966) MR0191693
15. J. M. Holtzman, On the maximum principle for non-linear discrete-time systems, IEEE Trans. Autom. Contr. AC-11 (1966), 4, 273-274. (1966) MR0191693
16. J. M. Holtzman H. Halkin, Directional convexity and the maximum principle for discrete systems, SIAM J. Control 4 (1966), 2, 263-275. (1966) MR0199008
17. H. Halkin, A maximum principle of the Pontryagin type for systems described by nonlinear difference equations, SIAM J. Control 4 (1966), 1, 90-111. (1966) Zbl0152.09301MR0199005
18. A. И. Пропой, Элементы теории оптимальных дискретных процессов, Наука, Москва 1973. (1973) Zbl1170.01397
19. C. Olech, Existence theorems for optimal problems with vector-valued cost function, Trans. Amer. Math. Soc. 136 (1969), 159-180. (1969) Zbl0179.14002MR0234338
20. B. Г. Болтянсий, Математические методы оптимального управления, Наука, Москва 1969. (1969) Zbl1149.62317
21. B. И. Благодатских, Достаточие условия оптимальности, Дифференциальные уравнения 9 (1973), 416-422. (1973) Zbl1170.01397MR0322626
22. W. F. Hogan, Point to set maps in mathematical programming, SIAM Review 15 (1973), 3, 591-603. (1973) Zbl0256.90042MR0345641
23. J. Doležal, Some properties of nonzero-sum multistage games, Preprints of the 6th IFIP Technical Conference on Optimization Techniques. Novosibirsk 1974. (1974) 
24. J. Doležal, Open-loop hierarchical solution of multistage games, Proceedings of the 2nd Formator Symposium, Prague 1974. Academia, Praha 1975. (1974) 
25. R. E. Bellman, Dynamic Programming, Princeton Univ. Press, Princeton, New Jersey 1957. (1957) Zbl0995.90618
26. G. Leitmann, An Introduction to Optimal Control, McGraw-Hill, New York 1966. (1966) Zbl0196.46302
27. S. A. W. Drew, The application of hierarchical control methods to a managerial problem, Int. J. Systems Sci. 6 (1975), 4, 371-395. (1975) Zbl0367.90057MR0424216
28. P. S. Ritch, Discrete optimal control with multiple constraints I.: Constraint separation and transformation technique, Automatica 9 (1973), 4, 415-429. (1973) Zbl0256.49034MR0439328
29. P. S. Ritch, Discrete optimal control with multiple constraints II: The batch crystallisation of sugar, Automatica 9 (1973), 4, 431-440. (1973) MR0439329

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