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Signomial dual Kuhn-tucker intervals

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Signomial programs are a special type of nonlinear programming problems which are especially useful in engineering design. This paper applies interval arithmetic, a generalization of ordinary arithmetic, to a dual equilibrium problem in signomial programming. Two constructive applications are considered. Application I involves uniqueness of local solutions; Application II involves existence and error bounds.

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  1. 1.

    Rijckaert, M. J., andMartens, X. M.,A Bibliographical Note on Geometric Programming, Journal of Optimization Theory and Applications, Vol. 26, No. 2, 1978.

  2. 2.

    Duffin, R. J., andPeterson, E. L.,Geometric Programming with Signomials, Journal of Optimization Theory and Applications, Vol. 11, pp. 3–35, 1973.

  3. 3.

    Passy, U., andWilde, D. J.,Generalized Polynomial Optimization, SIAM Journal on Applied Mathematics, Vol. 15, pp. 1344–1356, 1967.

  4. 4.

    Moore, R. E.,Interval Analysis, Prentice-Hall, Englewood Cliffs, New Jersey, 1966.

  5. 5.

    Hansen, E. R., andSmith, R.,A Computer Program for Solving a System of Linear Equations and Matrix Inversion with Automatic Error Bounding using Interval Arithmetic, Lockheed Missiles and Space Company, Report No. 4-22-66-3, 1966.

  6. 6.

    Passy, U. andWilde, D. J.,Mass Action and Polynomial Optimization, Journal of Engineering Mathematics, Vol. 3, pp. 325–335, 1969.

  7. 7.

    Falk, J. E.,Global Solutions of Signomial Programs, George Washington University, Program in Logistics, Technical Paper No. T-274, 1973.

  8. 8.

    Robinson, S. M.,Computable Error Bounds for Nonlinear Programming, Mathematical Programming, Vol. 5, pp. 235–242, 1973.

  9. 9.

    Duffin, R. J., Peterson, E. L., andZener, C.,Geometric Programming, John Wiley and Sons, New York, 1966.

  10. 10.

    Mancini, L. J., andPiziali, R. L.,Optimal Design of Helical Springs by Geometrical Programming, Engineering Optimization, Vol. 2, pp. 73–81, 1976.

  11. 11.

    Mancini, L. J.,Applications of Interval Arithmetic in Signomial Programming, Stanford University, PhD Thesis, 1975.

  12. 12.

    Wilde, D. J., andBeightler, C. S.,Foundations of Optimization, Prentice-Hall, Englewood Cliffs, New Jersey, 1967.

  13. 13.

    Zoltan, A. C.,Interval Arithmetic Subroutine Package for the IBM/360, Universidad Central de Venezuela, Facultad de Ciencias, Departamento de Computacion, Report No. 69-05, 1969.

  14. 14.

    Hansen, E. R., andSmith, R.,Interval Arithmetic in Matrix Computations, Part 2, SIAM Journal of Numerical Analysis, Vol. 4, pp. 1–9, 1967.

  15. 15.

    Hansen, E. R.,On Linear Algebraic Equations with Interval Coefficients, Topics in Interval Analysis, Edited by E. R. Hansen, Clarendon Press, Oxford, England, 1969.

  16. 16.

    Dembo, R. S.,Solution of Complementary Geometric Programs, Technion, Israel, MS Thesis, 1972.

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The authors are grateful to the National Science Foundation for support through a Graduate Fellowship and Grant No. GK-41301.

Communicated by M. Avriel

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Mancini, L.J., Wilde, D.J. Signomial dual Kuhn-tucker intervals. J Optim Theory Appl 28, 11–27 (1979).

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Key Words

  • Geometric programming
  • signomial programming
  • interval arithmetic
  • nonlinear equations
  • Newton's method