Previous article Next article On Second Order Necessary Conditions of OptimalityE. J. Messerli and E. PolakE. J. Messerli and E. Polakhttps://doi.org/10.1137/0307019PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] M. Canon, , C. Cullum and , E. Polak, Constrained minimization problems in finite-dimensional spaces, SIAM J. Control, 4 (1966), 528–547 10.1137/0304041 MR0207423 0145.34202 LinkGoogle Scholar[2] Lucien W. Neustadt, An abstract variational theory with applications to a broad class of optimization problems. I. General theory, SIAM J. Control, 4 (1966), 505–527 10.1137/0304040 MR0216349 0166.09401 LinkGoogle Scholar[3] Kenneth J. Arrow, , Leonid Hurwicz and , Hirofumi Uzawa, Constraint qualifications in masimization problems, Naval Res. Logist. Quart., 8 (1961), 175–191 MR0129481 0129.34103 CrossrefGoogle Scholar[4] I. M. Gelfand and , S. V. Fomin, Calculus of variations, Revised English edition translated and edited by Richard A. Silverman, Prentice-Hall Inc., Englewood Cliffs, N.J., 1963vii+232 MR0160139 Google Scholar[5] G. A. Bliss, Lectures on the Calculus of Variations, University of Chicago Press, Chicago, 1959 0036.34401 Google Scholar[6] Magnus R. Hestenes, Calculus of variations and optimal control theory, John Wiley & Sons Inc., New York, 1966xii+405 MR0203540 0173.35703 Google Scholar[7] Henry J. Kelley, , Richard E. Kopp and , H. Gardner Moyer, Singular extremalsTopics in Optimization, Academic Press, New York, 1967, 63–101 MR0215153 CrossrefGoogle Scholar[8] A. ya. Dubovickii and , A. A. Milyutin, Extremum problems with constraints, Soviet Math. Dokl., 4 (1963), 452–455 Google Scholar[9] A. Ja. Dubovickii˘ and , A. A. Miljutin, Second variations in extremal problems with constraints, Soviet Math. Dokl., 6 (1965), 12–16 MR0218943 Google Scholar[10] Garth P. McCormick, Second order conditions for constrained minima, SIAM J. Appl. Math., 15 (1967), 641–652 10.1137/0115056 MR0216866 0166.15601 LinkISIGoogle Scholar[11] H. W. Kuhn and , A. W. Tucker, Nonlinear programming, Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, 1950, University of California Press, Berkeley and Los Angeles, 1951, 481–492 MR0047303 Google Scholar[12] E. Polak and , E. J. Messerli, Second order conditions of optimality for constrained optimization problems in finite dimensional spaces, Memo., ERL-M224, Electronics Research Laboratory, University of California, Berkeley, 1967 Google Scholar[13] C. Berge, Topological Spaces, Macmillan, New York, 1963 Google Scholar[14] Lawrence M. Graves, The theory of functions of real variables, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1956xii+375 MR0075256 0070.05203 Google Scholar[15] J. Dieudonné, Foundations of modern analysis, Pure and Applied Mathematics, Vol. X, Academic Press, New York, 1960xiv+361 MR0120319 0100.04201 Google Scholar[16] R. E. Edwards, Functional analysis. Theory and applications, Holt, Rinehart and Winston, New York, 1965xiii+781 MR0221256 0182.16101 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails A Systematic Approach to Higher-Order Necessary Conditions in Optimization TheorySIAM Journal on Control and Optimization, Vol. 22, No. 2 | 17 February 2012AbstractPDF (3122 KB)Optimal Periodic Control: A General Theory of Necessary ConditionsSIAM Journal on Control and Optimization, Vol. 15, No. 5 | 1 August 2006AbstractPDF (3323 KB) Volume 7, Issue 2| 1969SIAM Journal on Control179-365 History Submitted:09 April 1968Published online:18 July 2006 InformationCopyright © 1969 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0307019Article page range:pp. 272-291ISSN (print):0036-1402Publisher:Society for Industrial and Applied Mathematics