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On the Global Convergence of a Modified Augmented Lagrangian Linesearch Interior-Point Newton Method for Nonlinear Programming

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Abstract

We consider a linesearch globalization of the local primal-dual interior-point Newton method for nonlinear programming introduced by El-Bakry, Tapia, Tsuchiya, and Zhang. The linesearch uses a new merit function that incorporates a modification of the standard augmented Lagrangian function and a weak notion of centrality. We establish a global convergence theory and present promising numerical experimentation.

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References

  1. LUSTIG, I., MARSTEN, R., and SHANNO, D., On Implementing Mehrotra's Predictor-Corrector Interior-Point Method for Linear Programming, SIAM Journal on Optimization, Vol, 2, pp. 435–449, 1992.

    Google Scholar 

  2. EL-BAKRY, A. S., TAPIA, R. A., TSUCHIYA, T., and ZHANG, Y., On the Formulation of the Primal-Dual Interior-Point Method for Nonlinear Programming, Journal of Optimization Theory and Applications, Vol. 89, pp. 507–541, 1996.

    Google Scholar 

  3. FIACCO, A. V., and McCORMICK, G. P., Nonlinear Programming; Sequential Unconstrained Minimization Techniques, John Wiley and Sons, New York, NY, 1968.

    Google Scholar 

  4. LASDON, L., YU, G., and PLUMMER, J., Primal-Dual and Primal Interior-Point Algorithms for General Nonlinear Programs, ORSA Journal on Computing, Vol. 7, 1995.

  5. MONTEIRO, R. C., PANG, J., and WANG, T., A Positive Algorithm for the Nonlinear Complementarity Problem, Technical Report, Department of Systems and Industrial Engineering. University of Arizona, Tucson, Arizona, 1992.

    Google Scholar 

  6. NASH, S. G. and SOFER, A., Linear and Nonlinear Programming, McGraw-Hill, New York, NY, 1996.

    Google Scholar 

  7. WRIGHT, M. H., Interior Methods for Constrained Optimization, Numerical Analysis Manuscript 91–10, AT&T Bell Laboratories, Murray Hill, New Jersey, 1991.

    Google Scholar 

  8. YAMASHITA, H., A Globally Convergent Primal-Dual Interior-Point Method for Constrained Optimization, Technical Report, Mathematical System Institute, Japan, 1992.

    Google Scholar 

  9. FORSGREN, A. and GILL, P., Primal-Dual Interior Methods for Nonconvex Nonlinear Programming, Technical Report NA-3, Department of Mathematics, University of California at San Diego, La Jolla, California, 1996.

    Google Scholar 

  10. BYRD, R. H., HRIBAR, M. B., and NOCEDAI, J., An Interior-Point Algorithm for Large-Scale Nonlinear Programming, Technical Report OTC 97/02, Northwestern University, 1997.

  11. GAY, D., OVERTON, M., and WRIGHT, M. H., An Interior-Point Algorithm for Solving General Nonlinear Programming Problems, Talk Presented at the 15th International Symposium on Mathematical Programming, Ann Arbor, Michigan, 1994.

  12. WRIGHT, M. H., Ill-Conditioning Computational Errors in Interior Methods for Nonlinear Programming, Technical Report 97–4–04, Computing Sciences Research, Bell Laboratories, Murray Hill, New Jersey, 1997.

    Google Scholar 

  13. ANSTREICHER, K. M., and VIAL, J., On the Convergence of an Infeasible Primal-Dual Interior-Point Method for Convex Programming, Optimizations Methods and Software, 1993.

  14. GONZALEZ-LIMA, M., TAPIA, R. A., and POTRA, F., On Effectively Computing the Analytic Center of the Solution Set by Primal-Dual Interior-Point Methods, SIAM Journal on Optimization, Vol. 8, pp. 1–25, 1998.

    Google Scholar 

  15. MARTINEZ, H. J., PARADA, Z., and TAPIA, R. A., On the Characterization of Q-Superlinear Convergence of Quasi-Newton Interior-Point Methods for Nonlinear Programming, Boletin de la Sociedad Mexicana de Matemáticas, Vol. 1, pp. 137–148, 1995.

    Google Scholar 

  16. DENNIS, J. E., Jr., and SCHNABEL, R. B., Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice-Hall, Englewood Cliffs, New Jersey, 1983 and SIAM, Philadelphia, Pennsylvania, 1996.

    Google Scholar 

  17. FADDEEVA, V. N., Computational Methods of Linear Algebra, Dover Publications, New York, NY, 1959.

    Google Scholar 

  18. ORTEGA, J. M., and RHEINBOLDT, W. C., Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, NY, 1970.

    Google Scholar 

  19. HOCK, W., and SCHITTKOWSKI, K., Test Examples for Nonlinear Programming Codes, Springer Verlag, New York, NY, 1981.

    Google Scholar 

  20. SCHITTKOWSKI, K., More Test Examples for Nonlinear Programming Codes, Springer Verlag, New York, NY, 1987.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematical Sciences, The University of Texas at El Paso, El Paso, Texas

    M. Argáez (Visiting Professor)

  2. Department of Computational and Applied Mathematics, Rice University, Houston, Texas

    R. A. Tapia (Professor)

Authors
  1. M. Argáez
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  2. R. A. Tapia
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Argáez, M., Tapia, R.A. On the Global Convergence of a Modified Augmented Lagrangian Linesearch Interior-Point Newton Method for Nonlinear Programming. Journal of Optimization Theory and Applications 114, 1–25 (2002). https://doi.org/10.1023/A:1015451203254

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