An Accelerated Gradient Projection Method for Linearly Constrained Nonlinear Estimation
David F. Shanno · SIAM Journal on Applied Mathematics · 1970
Previous article Next article An Accelerated Gradient Projection Method for Linearly Constrained Nonlinear EstimationD. F. ShannoD. F. Shannohttps://doi.org/10.1137/0118027PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Tom M. Apostol, Mathematical analysis: a modern approach to advanced calculus, Addison-Wesley Publishing Company, Inc., Reading, Mass., 1957, 73– MR0087718 (19,398e) 0077.05501 Google Scholar[2] Richard Bellman, Introduction to matrix analysis, McGraw-Hill Book Co., Inc., New York, 1960, 110–115 MR0122820 (23:A153) 0124.01001 Google Scholar[3] E. Bodewig, Matrix calculus, North-Holland Publishing Company, Amsterdam, 1956, 36–38 MR0080363 (18,235e) Google Scholar[4] Haskell B. Curry, The method of steepest descent for non-linear minimization problems, Quart. Appl. Math., 2 (1944), 258–261 MR0010667 (6,52b) 0061.26801 CrossrefGoogle Scholar[5] Saul I. Gass, Linear programming: methods and applications, McGraw-Hill Book Co., Inc., New York, 1958, 37–49 MR0096554 (20:3037) 0081.36702 Google Scholar[6] G. Hadley, Nonlinear and dynamic programming, Addison-Wesley Publishing Co., Inc., Reading, Mass.-London, 1964, 212–250 MR0173543 (30:3756) 0179.24601 Google Scholar[7] G. H. Hardy, , J. E. Littlewood and , G. Polya, Inequalities, Cambridge University Press, Cambridge, England, 1959, 76–77 Google Scholar[8] Kenneth Levenberg, A method for the solution of certain non-linear problems in least squares, Quart. Appl. Math., 2 (1944), 164–168 MR0010666 (6,52a) 0063.03501 CrossrefGoogle Scholar[9] Donald W. Marquardt, An algorithm for least-squares estimation of nonlinear parameters, J. Soc. Indust. Appl. Math., 11 (1963), 431–441 10.1137/0111030 MR0153071 (27:3040) 0112.10505 LinkISIGoogle Scholar[10] A. M. Mood and , F. A. Graybill, Introduction to the Theory of Statistics, McGraw-Hill, New York, 1963, 340–359 Google Scholar[11] D. D. Morrison, Methods for nonlinear least squares problems and convergence proofs, tracking programs and orbit determination, Proc. of the Jet Propulsion Laboratory Seminar, Jet Propulsion Laboratory, Pasadena, California, 1960, 1–9 Google Scholar[12] 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 (22:3601) 0099.36405 LinkISIGoogle Scholar[13] D. F. Shanno, Computational algorithm for linearly constrained nonlinear estimation, in preparation Google Scholar[14] J. F. Traub, Iterative methods for the solution of equations, Prentice-Hall Series in Automatic Computation, Prentice-Hall Inc., Englewood Cliffs, N.J., 1964, 17–22 MR0169356 (29:6607) 0121.11204 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Linear and Planar Array Factor SynthesisAntenna Arrays | 24 September 2010 Cross Ref BibliographyOptimization Techniques in Statistics | 1 Jan 1994 Cross Ref Algoritmo risolutivo per una classe particolare di problemi di minimo vincolatoCalcolo, Vol. 17, No. 2 | 1 Jun 1980 Cross Ref Minimization methods with constraintsJournal of Soviet Mathematics, Vol. 5, No. 1 | 1 Jan 1976 Cross Ref Annotated Bibliography on Generalized Inverses and ApplicationsGeneralized Inverses and Applications | 1 Jan 1976 Cross Ref A class of quadratically convergent algorithms for constrained function minimizationJournal of Optimization Theory and Applications, Vol. 16, No. 5-6 | 1 Sep 1975 Cross Ref Convergence of a regularized Gauss-Newton methodUSSR Computational Mathematics and Mathematical Physics, Vol. 13, No. 6 | 1 Jan 1973 Cross Ref Improved Newton's Load Flow Through a Minimization TechniqueIEEE Transactions on Power Apparatus and Systems, Vol. PAS-90, No. 5 | 1 Sep 1971 Cross Ref An Improved Marquardt Procedure for Nonlinear RegressionsTechnometrics, Vol. 13, No. 1 | 1 Feb 1971 Cross Ref Parameter Selection for Modified Newton Methods for Function MinimizationD. F. ShannoSIAM Journal on Numerical Analysis, Vol. 7, No. 3 | 14 July 2006AbstractPDF (692 KB)A Second Order Method for the Linearly Constrained Nonlinear Programming ProblemNonlinear Programming | 1 Jan 1970 Cross Ref Volume 18, Issue 2| 1970SIAM Journal on Applied Mathematics259-538 History Submitted:12 July 1968Published online:01 August 2006 InformationCopyright © 1970 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0118027Article page range:pp. 322-334ISSN (print):0036-1399ISSN (online):1095-712XPublisher:Society for Industrial and Applied Mathematics