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Global optimization using interval analysis — the multi-dimensional case

  • Algorithms for Non-Convergent Sequences
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Summary

We show how interval analysis can be used to compute the global minimum of a twice continuously differentiable function ofn variables over ann-dimensional parallelopiped with sides parallel to the coordinate axes. Our method provides infallible bounds on both the globally minimum value of the function and the point(s) at which the minimum occurs.

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References

  1. Dixon, L.C.W., Szegö, G.P.: Towards global optimization. Amsterdam: North Holland, 1975

    Google Scholar 

  2. Dixon, L.C.W., Szegö, G.P.: Towards global optimization 2. Amsterdam: North Holland, 1977

    Google Scholar 

  3. Hansen, Eldon: On solving systems of equations using interval arithmetic. Math. Comp.22, 374–384 (1968)

    Google Scholar 

  4. Hansen, Eldon: Interval forms of Newton's method. Computing20, 153–163 (1978)

    Google Scholar 

  5. Hansen, Eldon: Global optimization using interval analysis — the one-dimension case. Jour. Optimiz. Theo. Applic.29, 331–344 (1979)

    Google Scholar 

  6. Hansen, Eldon and Roberta Smith: Interval arithmetic in matrix computations, II. SIAM J. Num. Anal.4, 1–9 (1967)

    Google Scholar 

  7. Krawczyk, R.: Newton-Algorithmen zur Bestimmung von Nullstellen mit Fehlerschranken. Computing4, 187–201 (1969)

    Google Scholar 

  8. Moore, R.E.: Interval analysis. New York: Prentice-Hall (1966)

    Google Scholar 

  9. Moore, R.E.: On computing the range of a rational function ofn variables over a bounded region. Computing16, 1–15 (1976)

    Google Scholar 

  10. Moore, R.E.: A test for existence of solutions to nonlinear systems. SIAM J. Num. Anal.14, 611–615 (1977)

    Google Scholar 

  11. Moore, R.E.: A computational test for convergence of iterative methods for nonlinear systems. SIAM J. Num. Anal.15, 1194–1196 (1978)

    Google Scholar 

  12. Moore, R.E.: Methods and applications of interval analysis. Philadelphia: SIAM (1979)

    Google Scholar 

  13. Nickel, Karl: On the Newton method in interval analysis. Mathematics Research Center Report 1136, University of Wisconsin (1971)

  14. Skelboe, S.: Computation of rational interval functions, BIT,14, 87–95 (1974)

    Google Scholar 

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Authors and Affiliations

  1. Lockheed Missiles and Space Company, 94086, Sunnyvale, CA, USA

    Eldon Hansen

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  1. Eldon Hansen
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Hansen, E. Global optimization using interval analysis — the multi-dimensional case. Numer. Math. 34, 247–270 (1980). https://doi.org/10.1007/BF01396702

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  • DOI: https://doi.org/10.1007/BF01396702

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