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A formula on the approximate subdifferential of the difference of convex functions

Published online by Cambridge University Press:  17 April 2009

J.E. Martínez-legaz  and
A. Seeger
J.E. Martínez-legaz
Affiliation:
Dept. d'Economia i d'Història Econòmica, Universitat Autònoma de Barcelona, 08193-Bellaterra, Barcelona, Spain and Dept. de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, 08071 - Barcelona, Spain
A. Seeger
Affiliation:
Dept. de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, 08071 - Barcelona, Spain
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Abstract

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We give a formula on the ε−subdifferential of the difference of two convex functions. As a by-product of this formula, one recovers a recent result of Hiriart-Urruty, namely, a necessary and sufficient condition for global optimality in nonconvex optimisation.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 45 , Issue 1 , February 1992 , pp. 37 - 41
Copyright
Copyright © Australian Mathematical Society 1992

References

[1]Hiriart-Urruty, J.-B., ‘ε−subdifferential calculus’, in Convex analysis and optimization: Research Notes in Mathematics 57, pp. 43–92 (Pitman Publishers, 1982).Google Scholar
[2]Hiriart-Urruty, J.-B., ‘Generalized differentiability, duality and optimization for problems dealing with differences of convex functions’, in Convexity and duality in optimization: Lecture Notes in Econom, and Math. Systems 256, pp. 37–70 (Springer-Verlag, Berlin, Heidelberg, New York, 1986).CrossRefGoogle Scholar
[3]Hiriart-Urruty, J.-B., ‘From convex optimization to nonconvex optimization’, in Nonsmooth optimization and related topics, Editors Clarke, F.H., Demyanov, V.F., Giannessi, F., pp. 219–239 (Plenum Press, 1989).CrossRefGoogle Scholar
[4]Kutateladze, S. S., ‘Convex ε−programming’, Soviet Math. Dokl. 20 (1979), 391–393.Google Scholar
[5]Martínez-Legaz, J.-E., ‘Generalized conjugation and related topics’, in Generalized convexity and fractional programming with economic applications: Lect. Notes in Econom, and Math. Systems 345, pp. 198–218 (Springer-Verlag, Berlin, Heidelberg, New York, 1990).CrossRefGoogle Scholar
[6]Singer, I., ‘A Fenchel-Rockafellar type duality theorem for maximization’, Bull. Austral. Math. Soc. 29 (1979), 193–198.CrossRefGoogle Scholar
[7]Toland, J., ‘A duality principle for nonconvex optimization and the calculus of variations’, Arch. Rational Mech. Anal. 71 (1979), 41–61.CrossRefGoogle Scholar