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Dual problems of quasiconvex maximisation

Published online by Cambridge University Press:  17 April 2009

Alexander M. Rubinov  and
Belgin Şimşek
Alexander M. Rubinov
Affiliation:
Department of Mathematics and Computer Science Ben-GurionUniversity of the NegevBeer-Sheva 84105, Israel
Belgin Şimşek
Affiliation:
Mathematics DepartmentHacettepe University06532 Beytepe-Ankara, Turkey
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Abstract

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A conjugacy operation is introduced on the set Q(X) of all quasiconvex lower semicontinuous nonnegative functions vanishing at zero. This operation is used in order to introduce and study a dual problem with respect to a maximisation problem where both constraint and objective functions belong to Q(X).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 51 , Issue 1 , February 1995 , pp. 139 - 144
Copyright
Copyright © Australian Mathematical Society 1995

References

[1]Thach, R.T., ‘Quasiconjugates of functions, duality relationships between quasiconvex minimization under a reverse convex constraint and application’, J. Math. Anal. Appl. 159 (1991), 299–322.CrossRefGoogle Scholar
[2]Thach, R.T., ‘Global optimality criterion and a duality with zero gap in nonconvex optimization’, SIAM J. Math. Anal. 24 (1993), 1537–1556.CrossRefGoogle Scholar