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Convergence analysis for two-level algorithms of mathematical programming

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Part of the book series: Mathematical Programming Studies ((MATHPROGRAMM,volume 10))

Abstract

A general scheme, covering a wide class of two-level methods, is formulated. The possibilities for handling truncation errors and stopping rules on both levels are described. The convergence of the algorithm is proved under general assumptions, and computational results for an example of a minimax problem are given.

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References

  1. A. Auslender, “Minimization of convex functions with errors”, IX International Symposium on Mathematical Programming, Budapest, 1976.

    Google Scholar 

  2. P. Huard, “Optimization algorithms and point-to-set maps”, Mathematical Programming 8 (1975) 308–331.

    Article  MATH  MathSciNet  Google Scholar 

  3. J. Denel, “Nouvelles notions de continuité des applications multivoques et applications a l’optimisation”, Publication No 83 (mars 1977), Laboratoire de Calcul de l’Universite de Lille I.

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  4. R.R. Meyer, “The validity of a family of optimization methods”, SIAM Journal on Control 8 (1970) 41–54.

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  5. G. Pierra, “Crossing of algorithms in decomposition methods”, IFAC Symposium on Large Scale Systems Theory and Applications, Udine, 1976.

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  6. E. Polak, Computational methods in optimization (Academic Press, New York, 1971).

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  7. J. Szymanowski and A. Ruszczyński, “An accuracy selection algorithm for the modified gradient projection method in minimax problems”, 8th IFIP Conference on Optimization Techniques, Wurzburg, 1977.

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  8. W.I. Zangwill, “Nonlinear programming. A unified approach”, Prentice Hall, Englewood Cliffs, NJ, 1969).

    MATH  Google Scholar 

  9. “Methods for unconstrained optimization”, Technical Report I.2.03.2, Institute of Automatic Control, Technical University of Warsaw (1976).

    Google Scholar 

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P. Huard

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© 1979 The Mathematical Programming Society

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Szymanowski, J., Ruszczynski, A. (1979). Convergence analysis for two-level algorithms of mathematical programming. In: Huard, P. (eds) Point-to-Set Maps and Mathematical Programming. Mathematical Programming Studies, vol 10. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0120852

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  • DOI: https://doi.org/10.1007/BFb0120852

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00797-2

  • Online ISBN: 978-3-642-00798-9

  • eBook Packages: Springer Book Archive

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