An Efficient Computational Procedure for a Generalized Quadratic Programming Problem

Previous article Next article An Efficient Computational Procedure for a Generalized Quadratic Programming ProblemRobert O. BarrRobert O. Barrhttps://doi.org/10.1137/0307030PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Elmer G. Gilbert, An iterative procedure for computing the minimum of a quadratic form on a convex set, SIAM J. Control, 4 (1966), 61–80 10.1137/0304007 MR0189875 0196.51204 LinkGoogle Scholar[2] R. O. Barr, Masters Thesis, Computation of optimal controls by quadratic programming on convex reachable sets, Doctoral thesis, University of Michigan, 1966 Google Scholar[3] Robert O. Barr and , Elmer G. Gilbert, Some iterative procedures for computing optimal controlsAutomatic and remote control III (Proc. Third Congr. Internat. Federation Automat. Control (IFAC), London, 1966), Vol. 1, p. 47, Paper 24 D, Inst. Mech. Engrs., London, 1967, 9– MR0378410 Google Scholar[4] Marguerite Frank and , Philip Wolfe, An algorithm for quadratic programming, Naval Res. Logist. Quart., 3 (1956), 95–110 MR0089102 CrossrefGoogle Scholar[5] G. Hadley, Nonlinear and dynamic programming, Addison-Wesley Publishing Co., Inc., Reading, Mass.-London, 1964xi+484 MR0173543 0179.24601 Google Scholar[6] H. S. Houthakker, The capacity method of quadratic programming, Econometrica, 28 (1960), 62–87 MR0113723 0089.16001 CrossrefISIGoogle Scholar[7] S. Vajda, Mathematical programming, Addison-Wesley Series in Statistics, Addison-Wesley Publishing Co., Inc., Reading, Mass.-London, 1961ix+310 MR0135621 0102.36401 Google Scholar[8] Philip Wolfe, The simplex method for quadratic programming, Econometrica, 27 (1959), 382–398 MR0106783 0103.37603 CrossrefISIGoogle Scholar[9] Toshio Fujisawa and , Yutaka Yasuda, An iterative procedure for solving the time-optimal regulator problem, SIAM J. Control, 5 (1967), 501–512 10.1137/0305029 MR0222741 0178.10502 LinkGoogle Scholar[10] Lucien W. Neustadt, Synthesizing time optimal control systems, J. Math. Anal. Appl., 1 (1960), 484–493 10.1016/0022-247X(60)90015-9 MR0128573 0100.09903 CrossrefGoogle Scholar[11] Lucien W. Neustadt, Minimum effort control systems, J. SIAM Control Ser. A, 1 (1962), 16–31 10.1137/0301002 MR0145172 LinkGoogle Scholar[12] L. W. Neustadt, On synthesizing optimal controls, Proc. Second Congress of the International Federation of Automatic Control (IFAC), Butterworth, London, 1964 Google Scholar[13] J. H. Eaton, An iterative solution to time-optimal control, J. Math. Anal. Appl., 5 (1962), 329–344, 9 (1964), pp. 147–152 10.1016/S0022-247X(62)80015-8 MR0140800 0142.06801 CrossrefGoogle Scholar[14] Edward J. Fadden and , Elmer G. Gilbert, Computational aspects of the time-optimal control problemComputing Methods in Optimization Problems (Proc. Conf., Univ. California, Los Angeles, Calif., 1964), Academic Press, New York, 1964, 167–192 MR0168413 0161.07103 CrossrefGoogle Scholar[15] T. G. Babunashvili, The synthesis of linear optimal systems, SIAM J. Control, 2 (1964), 261–265 10.1137/0302023 LinkGoogle Scholar[16] V. F. Dem'janov, Construction of an optimum program in a linear system, Avtomat. i Telemeh., 25 (1964), 3–11 MR0189874 Google Scholar[17] C. Carathéodory, Über den variabilitätsbereich der Fourierschen konstanten von positiven harmonischen funktionen, Rend. Circ. Mat. Palermo, 32 (1911), 193–217 CrossrefGoogle Scholar[18] H. G. Eggleston, Convexity, Cambridge Tracts in Mathematics and Mathematical Physics, No. 47, Cambridge University Press, New York, 1958viii+136 MR0124813 0086.15302 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails On the Mathematical Foundations of Nondifferentiable Optimization in Engineering DesignE. Polak18 July 2006 | SIAM Review, Vol. 29, No. 1AbstractPDF (6593 KB)Iterative Procedures for Constrained and Unilateral Optimization ProblemsJ. Warga17 February 2012 | SIAM Journal on Control and Optimization, Vol. 20, No. 3AbstractPDF (1487 KB)Accelerated Frank–Wolfe AlgorithmsGerard G. L. Meyer1 August 2006 | SIAM Journal on Control, Vol. 12, No. 4AbstractPDF (877 KB)A Geometrically Convergent Algorithm for Solving Optimal Control ProblemsEarl R. Barnes18 July 2006 | SIAM Journal on Control, Vol. 10, No. 3AbstractPDF (769 KB)A New Iterative Procedure for the Minimization of a Quadratic Form on a Convex SetThomas Pecsvaradi and Kumpati S. Narendra18 July 2006 | SIAM Journal on Control, Vol. 8, No. 3AbstractPDF (466 KB) Volume 7, Issue 3| 1969SIAM Journal on Control History Submitted:02 April 1968Published online:18 July 2006 InformationCopyright © 1969 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0307030Article page range:pp. 415-429ISSN (print):0036-1402Publisher:Society for Industrial and Applied Mathematics