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The continuous method of steepest descent and its discretizations

  • Nonlinear And Stochastic Programming
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Optimization Techniques

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 7))

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References

  1. P.T. Boggs: The solution of Nonlinear Systems of Equations by Astable Integration Techniques; SIAM Journal on Numerical Analysis Vol. 8 (1971), pp. 767–785.

    Google Scholar 

  2. P.T. Boggs: The Convergence of the Ben-Israel Iteration for Nonlinear Least Squares Problems; Math. Comp. Vol. 30 (1976), pp. 512–522.

    Google Scholar 

  3. W.A. Coppel: Stability and Asymptotic Behaviour of Differential Equations; Heath, Boston, 1965.

    Google Scholar 

  4. J.E. Dennis, Jnr.: Non-linear Least Squares and Equations; in D. Jacobs (Ed.): The State of the Art in Numerical Analysis, Academic Press, London, 1977.

    Google Scholar 

  5. J. Kowalik, M.R. Osborne: Methods for Unconstrained Optimization Problems; Elsevier, New York, 1968.

    Google Scholar 

  6. P. Mitter: Minimization Methods based on A(O)-stable Runge-Kutta Processes; In W. Gröbner et. al.: The Method of Lie Series for Differential Equations and its Extensions; Techn. Report of the European Research Office, London, 1973.

    Google Scholar 

  7. P. Mitter, C.W. Ueberhuber: Analysis of Continuous Methods for Unconstrained Optimization and their Discretizations, Forschungsbericht Nr. 121, Institute for Advanced Studies, Vienna, 1977.

    Google Scholar 

  8. V.V. Nemytskii, V.V. Stepanov: Qualitative Theory of Differential Equations; Princeton University Press, 1960.

    Google Scholar 

  9. J.M. Ortega: Stability of Difference Equations and Convergence of Iterative Processes; SIAM Journal on Numerical Analysis Vol. 10 (1973), pp. 268–282.

    Google Scholar 

  10. J.M. Ortega, W.C. Rheinboldt: Interative Solution of Nonlinear Equations in Several Variables; Academic Press, New York, 1970.

    Google Scholar 

  11. L.F. Shampine: Stiffness and Nonstiff Differential Equation Solvers, II: Detecting Stiffness with Runge-Kutta Methods; ACM Trans. Math. Software Vol. 3 (1977), pp. 44–53.

    Google Scholar 

  12. C.W. Ueberhuber: Optimierung mittels kontinuierlicher Quasi-Newton-Verfahren und deren Diskretisierungen; Institut für Numerische Mathematik, TU-Wien, Bericht Nr. 19/76, Vienna, 1976.

    Google Scholar 

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Authors
  1. Peter Mitter
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  2. Christoph W. Ueberhuber
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Editor information

J. Stoer

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© 1978 Springer-Verlag

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Mitter, P., Ueberhuber, C.W. (1978). The continuous method of steepest descent and its discretizations. In: Stoer, J. (eds) Optimization Techniques. Lecture Notes in Control and Information Sciences, vol 7. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0006513

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  • DOI: https://doi.org/10.1007/BFb0006513

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08708-3

  • Online ISBN: 978-3-540-35890-9

  • eBook Packages: Springer Book Archive

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