Existence theorems for optimal problems with vector-valued cost function
HTML articles powered by AMS MathViewer
- by Czesław Olech
- Trans. Amer. Math. Soc. 136 (1969), 159-180
- DOI: https://doi.org/10.1090/S0002-9947-1969-0234338-5
- PDF | Request permission
References
- Lamberto Cesari, Existence theorems for weak and usual optimal solutions in Lagrange problems with unilateral constraints. I, Trans. Amer. Math. Soc. 124 (1966), 369–412. MR 203542, DOI 10.1090/S0002-9947-1966-0203542-1
- N. O. Da Cunha and E. Polak, Constrained minimization under vector-valued criteria in linear topological spaces, Mathematical Theory of Control (Proc. Conf., Los Angeles, Calif., 1967) Academic Press, New York, 1967, pp. 96–108. MR 0257847
- A. F. Filippov, On some questions in the theory of optimal regulation: existence of a solution of the problem of optimal regulation in the class of bounded measurable functions, Vestnik Moskov. Univ. Ser. Mat. Meh. Astr. Fiz. Him. 1959 (1959), no. 2, 25–32 (Russian). MR 0122650
- A. F. Filippov, Differential equations with multi-valued discontinuous right-hand side, Dokl. Akad. Nauk SSSR 151 (1963), 65–68 (Russian). MR 0151673
- Marc Q. Jacobs, Attainable sets in systems with unbounded controls, J. Differential Equations 4 (1968), 408–423. MR 227579, DOI 10.1016/0022-0396(68)90027-2
- Marc Q. Jacobs, Remarks on some recent extensions of Filippov’s implicit functions lemma, SIAM J. Control 5 (1967), 622–627. MR 0223951
- Victor Klee and Czesław Olech, Characterizations of a class of convex sets, Math. Scand. 20 (1967), 290–296. MR 236650, DOI 10.7146/math.scand.a-10839 K. Kuratowski, Les functions semi-continues dans l’espace des ensembles fermés, Fund. Math. 18 (1932), 148-166.
- K. Kuratowski and C. Ryll-Nardzewski, A general theorem on selectors, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 13 (1965), 397–403 (English, with Russian summary). MR 188994
- A. Lasota and C. Olech, On the closedness of the set of trajectories of a control system, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 14 (1966), 615–621 (English, with Russian summary). MR 209034
- E. B. Lee and L. Markus, Optimal control for nonlinear processes, Arch. Rational Mech. Anal. 8 (1961), 36–58. MR 128571, DOI 10.1007/BF00277429 E. J. McShane, Existence theorems for ordinary problems of the calculus of variations, Ann. Scuola Norm Sup. Pisa 3 (1934), 181-211. M. Nagumo, Über die gleichmassige Summierbarkeit und ihre Anwendung auf ein Variations-problem, Japan. J. Math. 6 (1929), 178-182.
- A. Pliś, Measurable orientor fields, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 13 (1965), 565–569. MR 194715
- Emilio Roxin, The existence of optimal controls, Michigan Math. J. 9 (1962), 109–119. MR 136844 L. Tonneli, Sugli integrali del calcolo delle variazioni in forma ordinaria, Ann. Scuola Norm Sup. Pisa 3 (1934), 401-450; Opere scelte. vol. 3, Edizioni Cremonese, Rome, 1962, pp. 192-254.
- T. Ważewski, On an optimal control problem, Differential Equations and Their Applications (Proc. Conf., Prague, 1962) Publ. House Czech. Acad. Sci., Prague; Academic Press, New York, 1965, pp. 229–242. MR 0201758
Bibliographic Information
- © Copyright 1969 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 136 (1969), 159-180
- MSC: Primary 49.20
- DOI: https://doi.org/10.1090/S0002-9947-1969-0234338-5
- MathSciNet review: 0234338