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Non differentiable symmetric duality

  • Bertram Mond (a1) (a2) (a3) and Murray Schechter (a1) (a2) (a3)

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In this paper we construct dual pairs of problems, of both the Wolfe and Mond-Weir types, in which the objective contains a a support function and is therefore not differentiable. A special case which appears repeatedly in the literature is that in which the support function is the square root of a positive semidefinite quadratic form. This and other special cases can be readily generated from our result.

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References

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[1]Clarke, F.H., Optimization and nonsmooth analysis (Wiley, New York, 1983).
[2]Chandra, S., Craven, B.D. and Mond, B., ‘Generalized concavity and duality with a square root term’, in Mathematische Operationsforschung und Statistic Series optimization 16, 1975, pp. 653662.
[3]Chandra, S. and Husain, I., ‘Symmetric dual nondifferentiable programsBull. Autral. Math. Soc. 24 (1981), 295307.
[4]Demyanov, V.F. and Dixon, L.C.W., Quasidifferential calculus, Math. Prog. Study 29 (North-Holland, Amsterdam, 1986).
[5]Mond, B. and Weir, T., ‘Generalized concavity and duality’ in Generalized concavity in optimization and economics, (Schiable, S. and Ziemba, W.T., Editors) (Academic Press, New York, 1981).
[6]Schechter, M., ‘More on subgradient dualityJ. Math. Anal. Appl. 71 (1979), 251262.
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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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