Portal de Periódicos da CAPES

On Variational Theory and Optimal Control Theory

1965; Society for Industrial and Applied Mathematics; Volume: 3; Issue: 1 Linguagem: Inglês

10.1137/0303003

2168-359X

Magnus R. Hestenes,

Heat Transfer and Mathematical Modeling

Previous article Next article On Variational Theory and Optimal Control TheoryMagnus R. HestenesMagnus R. Hesteneshttps://doi.org/10.1137/0303003PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Gilbert A. Bliss, Lectures on the Calculus of Variations, University of Chicago Press, Chicago, Ill., 1946ix+296 MR0017881 (8,212e) 0063.00459 Google Scholar[2] M. R. Hestenes, A general problem in the calculus of variations with applications to paths of least time, RM-100, The RAND Corporation, Santa Monica, California, 1949, see also ASTIA Document 112382 Google Scholar[3] L. S. Pontryagin, , V. G. Boltyanskii, , R. V. Gamkrelidze and , E. F. Mishchenko, The mathematical theory of optimal processes, Translated from the Russian by K. N. Trirogoff; edited by L. W. Neustadt, Interscience Publishers John Wiley & Sons, Inc. New York-London, 1962viii+360 MR0166037 (29:3316b) 0102.32001 Google Scholar[4] E. J. McShane, On multipliers for Lagrange problems, Amer. J. Math., 61 (1939), 809–819 MR0000462 (1,78a) 0022.23403 CrossrefGoogle Scholar[5] Lawrence M. Graves, On the Weierstrass condition for the problem of Bolza in the calculus of variations, Ann. of Math. (2), 33 (1932), 747–752 MR1503088 0005.29803 CrossrefGoogle Scholar[6] Leonard D. Berkovitz, Variational methods in problems of control and programming, J. Math. Anal. Appl., 3 (1961), 145–169 10.1016/0022-247X(61)90013-0 MR0139030 (25:2470) 0100.31005 CrossrefGoogle Scholar[7] F. A. Valentine, Masters Thesis, The problem of Lagrange with differential inequalities as added side conditions, Dissertation, University of Chicago, Chicago, 1937 Google Scholar[8] T. Guinn, Masters Thesis, On first order necessary conditions for variational and optimal control problems, Dissertation, University of California, Los Angeles, 1964 Google Scholar[9] L. L. Pennisi, Masters Thesis, An indirect sufficiency proof for the problem of Lagrange with differential inequalities as added side conditions, Dissertation, University of Chicago, Chicago, 1952 Google Scholar[10] E. H. Mookini, Masters Thesis, Necessary conditions and sufficient conditions for the problem of Bolza in the calculus of variations, Dissertation, University of California, Los Angeles, 1964 Google Scholar[11] E. J. McShane, Sufficient conditions for a weak relative minimum in the problem of Bolza, Trans. Amer. Math. Soc., 52 (1942), 344–379 MR0006828 (4,48d) 0063.03871 CrossrefGoogle Scholar[12] Magnus R. Hestenes, An indirect sufficiency proof for the problem of Bolza in nonparametric form, Trans. Amer. Math. Soc., 62 (1947), 509–535 MR0023465 (9,360c) 0032.02004 CrossrefISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Necessary Optimality Conditions for Optimal Control Problems with Equilibrium ConstraintsLei Guo and Jane J. Ye11 October 2016 | SIAM Journal on Control and Optimization, Vol. 54, No. 5AbstractPDF (367 KB)Sufficient Conditions for Global Minima of Suitably Convex Functionals from Variational and Control TheoryGeorge M. Ewing2 August 2006 | SIAM Review, Vol. 19, No. 2AbstractPDF (2098 KB)Optimal Control Problems with Mixed Control-Phase Variable Equality and Inequality ConstraintsKarol Makowski and Lucien W. Neustadt18 July 2006 | SIAM Journal on Control, Vol. 12, No. 2AbstractPDF (3891 KB)Some Sufficient Conditions for Optimality in Control Problems with State Space ConstraintsJ. E. Funk and E. G. Gilbert18 July 2006 | SIAM Journal on Control, Vol. 8, No. 4AbstractPDF (648 KB)Differential Games with DelayA. Halanay18 July 2006 | SIAM Journal on Control, Vol. 6, No. 4AbstractPDF (830 KB)Optimal Controls for Systems with Time LagA. Halanay18 July 2006 | SIAM Journal on Control, Vol. 6, No. 2AbstractPDF (1137 KB)An Abstract Variational Theory with Applications to a Broad Class of Optimization Problems. II. ApplicationsLucien W. Neustadt18 July 2006 | SIAM Journal on Control, Vol. 5, No. 1AbstractPDF (4366 KB)On Some Extremal Problems in the Theory of Differential Equations with Applications to the Theory of Optimal ControlR. V. Gamkrelidze1 August 2006 | Journal of the Society for Industrial and Applied Mathematics Series A Control, Vol. 3, No. 1AbstractPDF (1828 KB)The Problem of Bounded Space Coordinates as a Problem of HestenesT. Guinn18 July 2006 | Journal of the Society for Industrial and Applied Mathematics Series A Control, Vol. 3, No. 2AbstractPDF (729 KB)Weakened Hypotheses for the Variational Problem Considered by HestenesT. Guinn18 July 2006 | Journal of the Society for Industrial and Applied Mathematics Series A Control, Vol. 3, No. 3AbstractPDF (485 KB) Volume 3, Issue 1| 1965Journal of the Society for Industrial and Applied Mathematics Series A Control History Submitted:14 September 1964Accepted:04 December 1964Published online:01 August 2006 InformationCopyright © 1965 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0303003Article page range:pp. 23-48ISSN (print):0887-4603ISSN (online):2168-359XPublisher:Society for Industrial and Applied Mathematics