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Numerical Experiences with New Truncated Newton Methods in Large Scale Unconstrained Optimization

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Abstract

Recently, in [12] a very general class oftruncated Newton methods has been proposed for solving large scale unconstrained optimization problems. In this work we present the results of an extensive numericalexperience obtained by different algorithms which belong to the preceding class. This numerical study, besides investigating which arethe best algorithmic choices of the proposed approach, clarifies some significant points which underlies every truncated Newton based algorithm.

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References

  1. I. Bongartz, A. Conn, N. Gould, and P. Toint. CUTE: Constrained and unconstrained testing environment. ACM Transaction on Mathematical Software, 21:123–160, 1995.

    Google Scholar 

  2. A. Conn, N. Gould, and P. Toint. LANCELOT: A Fortran package for Large-Scale Nonlinear Optimization (Release A). Springer Verlag, Heidelberg, Berlin, 1992.

    Google Scholar 

  3. J. Cullum and R. Willoughby. Lanczos alghorithms for large symmetric eigenvalue computations. Birkhauser, Boston, 1985.

    Google Scholar 

  4. R. Dembo, S. Eisenstat, and T. Steihaug. Inexact Newton methods. SIAM Journal on Numerical Analysis, 19:400–408, 1982.

    Google Scholar 

  5. R. Dembo and T. Steihaug. Truncated-Newton methods algorithms for large-scale unconstrained optimization. Mathematical Programming, 26:190–212, 1983.

    Google Scholar 

  6. N. Deng, Y. Xiao, and F. Zhou. Nonmonotonic trust region algorithm. Journal of Optimization Theory and Applications, 76:259–285, 1993.

    Google Scholar 

  7. M. Ferris, S. Lucidi, and M. Roma. Nonmonotone curvilinear linesearch methods for unconstrained optimization. Computational Optimization and Applications, 6: 117–136, 1996.

    Google Scholar 

  8. G. Golub and C. Van Loan. Matrix Computations. The John Hopkins Press, Baltimore, 1989.

    Google Scholar 

  9. L. Grippo, F. Lampariello, and S. Lucidi. A truncated Newton method with nonmonotone linesearch for unconstrained optimization. Journal of Optimization Theory and Applications, 60:401–419, 1989.

    Google Scholar 

  10. L. Grippo, F. Lampariello, and S. Lucidi. A class of nonmonotone stabilization methods in unconstrained optimization. Numerische Mathematik, 59:779–805, 1991.

    Google Scholar 

  11. G. Liu and J. Han. Convergence of the BFGS algorithm with nonmonotone linesearch. Technical report, Institute of Applied Mathematics, Academia Sinica, Beijing, 1993.

    Google Scholar 

  12. S. Lucidi, F. Rochetich, and M. Roma. Curvilinear stabilization techniques for truncated Newton methods in large scale unconstrained optimization: the complete results. Technical Report 02.95, Dipartimento di Informatica e Sistemistica, Università di Roma "La Sapienza", 1995.

    Google Scholar 

  13. G. McCormick. A modification of Armijo's step-size rule for negative curvature. Mathematical Programming, 13:111–115, 1977.

    Google Scholar 

  14. J. Moré and D. Sorensen. On the use of directions of negative curvature in a modified Newton method. Mathematical Programming, 16:1–20, 1979.

    Google Scholar 

  15. S. Nash. Newton-type minimization via Lanczos method. SIAM Journal on Numerical Analysis, 21:770–788, 1984.

    Google Scholar 

  16. S. Nash and J. Nocedal. A numerical study of the limited memory BFGS method and the truncated-Newton method for large scale optimization. SIAM Journal on Optimization, 1:358–372, 1991.

    Google Scholar 

  17. C. Paige and M. Saunders. Solution of sparse indefinite systems of linear equations. SIAM Journal on Numerical Analysis, 12:617–629, 1975.

    Google Scholar 

  18. B. Parlett. The symmetric eigenvalue problem. Prentice-Hall series in Computational Mathematics, Englewood Cliffs, 1980.

  19. T. Schlick and A. Fogelson. TNPACK-A truncated Newton package for large-scale problems: I. algorithm and usage. ACM Transaction on Mathematical Software, 18:46–70, 1992.

    Google Scholar 

  20. G. Shultz, R. Schnabel, and R. Byrd. A family of trust-region-based algorithms for unconstrained minimization. SIAM Journal on Numerical Analysis, 22:47–67, 1985.

    Google Scholar 

  21. P. Toint. An assesment of non-monotone linesearch techniques for unconstrained optimization. SIAM Journal of Scientific Computing, 17: 725–739, 1996.

    Google Scholar 

  22. P. Toint. A non-monotone trust-region algorithm for nonlinear optimization subject to convex constraints. Technical Report 94/24, Department of Mathematics, FUNDP, Namur, Belgium, 1994.

    Google Scholar 

  23. Y. Xiao and F. Zhou. Nonmonotone trust region methods with curvilinear path in unconstrained minimization. Computing, 48:303–317, 1992.

    Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Informatica e Sistemistica, Università di Roma “La Sapienza”, Roma, Italy

    Massimo Roma

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  1. Stefano Lucidi
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  2. Massimo Roma
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Lucidi, S., Roma, M. Numerical Experiences with New Truncated Newton Methods in Large Scale Unconstrained Optimization. Computational Optimization and Applications 7, 71–87 (1997). https://doi.org/10.1023/A:1008619812615

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