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On Rosen's gradient projection methods

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Abstract

This paper is a survey of Rosen's projection methods in nonlinear programming. Through the discussion of previous works, we propose some interesting questions for further research, and also present some new results about the questions.

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References

  1. M. Avriel,Nonlinear Programming: Analysis and Methods (Prentice-Hall, Englewood Cliffs, NJ, 1986).

    Google Scholar 

  2. M.S. Bazaraa and C.M. Shetty,Nonlinear Programming: Theory and Algorithms (Wiley, New York, 1979).

    Google Scholar 

  3. D.-Z. Du, A modification of Rosen-Polak's algorithm, Kexue Tonbao 28(1983)301–305, in Chinese.

  4. D.-Z. Du and X.-S. Zhang, A convergence theorem for Rosen's gradient projection method, Math. Progr. 36(1986)135–144.

    Google Scholar 

  5. D.-Z. Du and X.-S. Zhang, Global convergence of Rosen's gradient projection method, Math. Progr. 44(1989)357–366.

    Google Scholar 

  6. D.-Z. Du, Remarks on the convergence of Rosen's gradient projection method, Acta Math. Appl. Sinica (English Series) 3(1987)270–279.

    Google Scholar 

  7. D.-Z. Du, J. Sun and T.-T. Song, A counterexample for Rosen's gradient projection method, Mathematical Report, Institute of Applied Mathematics, Beijing (1980), in Chinese.

    Google Scholar 

  8. D.-Z. Du and X.-S. Zhang, Notes on a new gradient projection method, Syst. Sci. Math. Sci. 2 (2) (1989)184–192.

    Google Scholar 

  9. D.-Z. Du, A gradient projection method for convex programming with nonlinear constraints, Acta. Math. Appl. Sinica 8(1985)7–16, in Chinese.

    Google Scholar 

  10. D. Goldfarb, Extension of Davidon's variable metric method to maximization under linear inequality and equality constraints, SIAM J. Appl. Math. 17(1969)739–764.

    Google Scholar 

  11. D. Goldfarb and L. Lapidus, Conjugate gradient method for nonlinear programming problems with linear constraints, Industr. Engin. Chem. Fundamentals 7(1968)142–151.

    Google Scholar 

  12. X.-Y. Gui and D.-Z. Du, A superlinearly convergent method to the linearly contrained optimization problem under degeneracy, Acta Math. Appl. Sinica (English Series) 1(1984)76–84.

    Google Scholar 

  13. G.-Z. He, Proof for convergence of Rosen's gradient projection method, Technical Report, Chengdu University of Technology and Science (1986), in Chinese.

  14. H.-Y. Kwei (Gui), F. Wu and Y.-L. Lai, Extension of a variable metric algorithm to a linearly constrained optimization problem — a variation of Goldfarb's algorithm, in:Operations Research 1978, ed. K.B. Haley (North-Holland, 1979).

  15. Y.-L. Lai, An algorithm and its convergence for nonlinear constrained convex programming, Acta Math. Sinica 3(1980)332–331, in Chinese.

    Google Scholar 

  16. D.G. Luenberger,Introduction to Linear and Nonlinear Programming (Addison-Wesley, Reading, MA, 1973).

    Google Scholar 

  17. E. Polak, On the convergence of optimization algorithms, Rev. Française d'Informatique et de Recherche Operationelle 3(1969)17–34.

    Google Scholar 

  18. E. Polak,Computational Methods in Optimization (Academic Press, New York, 1971).

    Google Scholar 

  19. K. Ritter, Convergence and superlinear convergence of algorithms for linearly constrained minimization problems, in:Nonlinear Optimization: Theory and Algorithms, Part 2, ed. L.C.W. Dixon, E. Spedicado and G.P. Szegö (1980).

  20. J.B. Rosen, The gradient projection method for nonlinear programming, Part 1: Linear constraints, SIAM J. Appl. Math. 8(1960)181–217.

    Google Scholar 

  21. J.B. Rosen, The gradient projection method for nonlinear programming, Part 2: Nonlinear constraints, SIAM J. Appl. Math. 9(1961)514–553.

    Google Scholar 

  22. M. Yue and J. Han, A new reduced gradient method, Scientia Sinica 22(1979)1099–1113.

    Google Scholar 

  23. X.-S. Zhang, An improved Rosen-Polak method, Acta Math. Appl. Sinica 2(1979)257–267, in Chinese.

    Google Scholar 

  24. X.-S. Zhang, Discussion on Polak's algorithm of nonlinear programming, Acta Math. Appl. Sinica 4(1981)1–13, in Chinese.

    Google Scholar 

  25. X.-S. Zhang, On the convergence of Rosen's gradient projection method, Acta Math. Appl. Sinica 8(1985)125–128, in Chinese. [Acta Math. Appl. Sinica (English Series) 3(1987)280–288].

    Google Scholar 

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This work was supported in part by the National Science Foundation of China.

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Du, D.Z., Wu, F. & Zhang, X.S. On Rosen's gradient projection methods. Ann Oper Res 24, 9–28 (1990). https://doi.org/10.1007/BF02216813

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