Extension of Davidon’s Variable Metric Method to Maximization Under Linear Inequality and Equality Constraints

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Previous article Next article Extension of Davidon's Variable Metric Method to Maximization Under Linear Inequality and Equality ConstraintsDonald GoldfarbDonald Goldfarbhttps://doi.org/10.1137/0117067PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] M. J. Box, A comparison of several current optimization methods, and the use of transformations in constrained problems, Comput. J., 9 (1966), 67–77 MR0192645 0146.13304 CrossrefISIGoogle Scholar[2] Charles W. Carroll, The created response surface technique for optimizing nonlinear, restrained systems, Operations Res., 9 (1961), 169–185 MR0129020 0111.17004 CrossrefISIGoogle Scholar[3] R. Courant and , D. Hilbert, Methods of mathematical physics. Vol. I, Interscience Publishers, Inc., New York, N.Y., 1953xv+561 MR0065391 0051.28802 Google Scholar[4] W. C. Davidon, Variable metric method for minimization, Atomic Energy Commission Research Development Report, ANL-5990, 1959 Google Scholar[5] Jack B. Dennis, Mathematical programming and electrical networks, The Technology Press of The Massachusetts Institute of Technology, Cambridge, Mass., 1959vi+186 MR0108400 Google Scholar[6] V. N. Faddeeva, Computational methods of linear algebra, Dover Publications Inc., New York, 1959xi+252 MR0100344 0086.10802 Google Scholar[7] A. V. Fiacco and , G. P. McCormick, Programming under nonlinear constraints by unconstrained minimization: A primal-dual method, Tech. Paper, RAC-TP-96, Research Analyses Corporation, 1963 Google Scholar[8] A. V. Fiacco and , G. P. McCormick, The sequential unconstrained minimization technique for nonlinear programming, a primaldual method, Management Sci, 10 (1964), 360–366 CrossrefISIGoogle Scholar[9] A. V. Fiacco and , G. P. McCormick, Computational algorithm for the sequential unconstrained minimization technique for nonlinear programming, Management Sci, 10 (1964), 601–617 CrossrefISIGoogle Scholar[10] A. V. Fiacco and , G. P. McCormick, Extensions of the sequential unconstrained minimization technique (SUMT) for nonlinear programming, presented at the American Meeting of the Institute of Management Sciences, San Francisco, 1965 Google Scholar[11] R. Fletcher and , M. J. D. Powell, A rapidly convergent descent method for minimization, Comput. J., 6 (1963/1964), 163–168 MR0152116 0132.11603 CrossrefISIGoogle Scholar[12] R. Fletcher and , C. M. Reeves, Function minimization by conjugate gradients, Comput. J., 7 (1964), 149–154 10.1093/comjnl/7.2.149 MR0187375 0132.11701 CrossrefISIGoogle Scholar[13] R. Frisch, The multiplex method for linear programming, Memorandum, Universetetets Socialo-konomisk Institute, Oslo, 1958 Google Scholar[14] Saul I. Gass, Linear programming: Methods and applications, Second edition, McGraw-Hill Book Co., New York, 1964xii+280 MR0195573 Google Scholar[15] D. Goldfarb, Masters Thesis, A conjugate gradient method for nonlinear programming, Doctoral thesis, Department of Chemical Engineering, Princeton University, 1966 Google Scholar[16] D. Goldfarb and , L. Lapidus, Conjugate gradient method for nonlinear programming problems with linear constraints, Industrial and Engineering Chemistry Fundamentals, 7 (1968), 142–151 10.1021/i160025a024 CrossrefISIGoogle Scholar[17] G. Hadley, Nonlinear and dynamic programming, Addison-Wesley Publishing Co., Inc., Reading, Mass.-London, 1964xi+484 MR0173543 0179.24601 Google Scholar[18] Paul R. Halmos, Finite-dimensional vector spaces, The University Series in Undergraduate Mathematics, D. Van Nostrand Co., Inc., Princeton-Toronto-New York-London, 1958viii+200 MR0089819 0107.01404 Google Scholar[19] 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 0044.05903 Google Scholar[20] C. E. Lemke, The constrained gradient method of linear programming, J. Soc. Indust. Appl. Math., 9 (1961), 1–17 10.1137/0109001 MR0121247 0112.12302 LinkISIGoogle Scholar[21] Clair E. Miller, R. L. Graves and , P. Wolfe, The simplex method for local separable programmingRecent advances in mathematical programming, McGraw-Hill, New York, 1963, 89–100 MR0171624 0232.90060 Google Scholar[22] M. J. D. Powell, An iterative method for finding stationary values of a function of several variables, Comput. J, 5 (1962), 147–151 0104.34303 CrossrefGoogle Scholar[23] M. J. D. Powell, An efficient method for finding the minimum of a function of several variables without calculating derivatives, Comput. J., 7 (1964), 155–162 10.1093/comjnl/7.2.155 MR0187376 0132.11702 CrossrefISIGoogle Scholar[24] J. B. Rosen, The gradient projection method for nonlinear programming. I. Linear constraints, J. Soc. Indust. Appl. Math., 8 (1960), 181–217 10.1137/0108011 MR0112750 0099.36405 LinkISIGoogle Scholar[25] H. H. Rosenbrock, An automatic method for finding the greatest or least value of a function, Comput. J., 3 (1960