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Non differentiable symmetric duality

Published online by Cambridge University Press:  17 April 2009

Bertram Mond  and
Murray Schechter
Bertram Mond
Affiliation:
Department of MathematicsLa Trobe UniversityBundoora Vic 3083Australia Department of MathematicsLehigh UniversityBethlehem PA 18105United States of America Department of MathematicsLehigh UniversityBethlehem PA 18105United States of America
Murray Schechter
Affiliation:
Department of MathematicsLa Trobe UniversityBundoora Vic 3083Australia Department of MathematicsLehigh UniversityBethlehem PA 18105United States of America Department of MathematicsLehigh UniversityBethlehem PA 18105United States of America
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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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 53 , Issue 2 , April 1996 , pp. 177 - 188
Copyright
Copyright © Australian Mathematical Society 1996

References

[1]Clarke, F.H., Optimization and nonsmooth analysis (Wiley, New York, 1983).Google Scholar
[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. 653–662.Google Scholar
[3]Chandra, S. and Husain, I., ‘Symmetric dual nondifferentiable programs’ Bull. Autral. Math. Soc. 24 (1981), 295–307.CrossRefGoogle Scholar
[4]Demyanov, V.F. and Dixon, L.C.W., Quasidifferential calculus, Math. Prog. Study 29 (North-Holland, Amsterdam, 1986).CrossRefGoogle Scholar
[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).Google Scholar
[6]Schechter, M., ‘More on subgradient duality’ J. Math. Anal. Appl. 71 (1979), 251–262.CrossRefGoogle Scholar