Publication Cover
Applicable Analysis
An International Journal
Volume 8, 1979 - Issue 4
23
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

A Homotopy based approach to unconstrained optimization

Pages 319-336 | Published online: 02 Nov 2010

References

  • Armijo , L. 1966 . Minimization of functions having Lipschitz continuous first partial derivatives . Pacific J. Math. , 16 : 1 – 3 .
  • Boggs , P. T. 1971 . The solution of nonlinear systems of equations by A-stable integration technique . SIAM J. Numer. Anal. , 8 : 767 – 784 .
  • Broyden , C. G. 1967 . Quasi-Newton methods and their applications to function minimization . Maths. ofComp. , 21 : 368 – 381 .
  • Broyden , C. G. 1970 . “ Recent developments in solving nonlinear algebraic systems. ” . In Numerical Methods for Nonlinear Algebraic Equations , Edited by: Rabinowitz , P. London : Gordon and Breach .
  • Davidenko , D. F. 1953 . On a new method of numerical solution of systems of nonlinear equations . Dokl. Akad. Nauk USSR (N.S.) , 88 : 601 – 602 .
  • Dennis , J. E. and Mei , H. H. W. 1975. . “ An unconstrained optimization algorithm which uses function and gradient values, T.R. ” . 75 – 246 . Department of Computer Science, Cornell University .
  • Fiacco , A. V. and McCormick , G. P. 1968 . Nonlinear Programming: Sequential Unconstrained Minimization Techniques. , New York : John Wiley and Sons .
  • Fletcher , R. 1970 . A new approach to variable metric algorithms . Computer Journal , 13 : 317 – 322 .
  • Goldfeld , S. M. , Quandt , R. E. and Trotter , H. F. 1966 . Maximization by quadratic hill climbing, Econometrica . 34 : 541 – 551 .
  • Hebden , M. D. “ An algorithm for minimization using exact second derivatives. ” . Report T.P. 515, A.E.R.E.
  • Levenberg , K. 1944 . A method for the solution of certain non-linear problems in least squares . Quart. Appl Math. , 2 : 164 – 168 .
  • Luenberger , D. G. 1973 . Introduction to Linear and Nonlinear Programming , Reading, Mass : Addison-Wesley .
  • Marquardt , D. W. 1963 . An algorithm for least squares estimation of nonlinear parameters . J. Soc. Indust. Appl. Math. , 11 : 431 – 441 .
  • Meyer , G. H. 1968 . On solving nonlinear equations with a one-parameter operator imbed-ding . SIAM J. Numer. Anal. , 5 : 739 – 752 .
  • Michael , E. 1970 . “ A survey of continuous selections ” . In Lecture Notes in Mathematics , Vol. 171 , 54 – 58 . New York : Springer-Verlag .
  • Murtagh , B. A. and Sargent , R. W. H. 1969 . “ A constrained minimization method with quadratic convergence. ” . In Optimization , Edited by: Fletcher , R. 215 – 246 . New York : Academic Press .
  • Ortega , J. M. and Rheinboldt , W. C. 1970 . Iterative Solution of Nonlinear Equations in Several Variables , New York : Academic Press .
  • Ostrowski , A. M. 1973 . Solutions of Equations in Euclidean and Banach Spaces , New York : Academic Press .
  • Powell , M. J. D. 1970 . “ A hybrid method for nonlinear equations. ” . In Numerical Methods for Nonlinear Algebraic Equations , Edited by: Rabinowitz , P. London : Gordon and Breach .
  • Powell , M. J. D. 1970 . “ A FORTRAN subroutine for solving systems of nonlinear algebraic equations. ” . In Numerical Methods for Nonlinear Algebraic Equations , Edited by: Rabinowitz , P. London : Gordon and Breach .
  • Powell , M. J. D. 1970 . “ A new algorithm for unconstrained optimization. ” . In Nonlinear Programming , Edited by: Rosen , J. B. , Mangasarian , O. L. and Ritter , K. New York : Academic Press .
  • Powell , M. J. D. “ A view of unconstrained optimization. ” . Report C.S.S. 14, A.E.R.E.
  • Tapia , R. A. 1974 . A stable approach to Newton's method for general mathematical programming problems in Rn . J. Optimization Theory , 14 : 453 – 476 .
  • Varga , R. S. Matrix Iterative Analysis
  • Vial , J. P. and Zang , I. June 1975 . “ Unconstrained optimization by approximation of the gradient path, CORE Discussion Paper No. 7513 ” . June , Université Cathohque de Louvain .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.