Duality is studied for a minimization problem with finitely many inequality and equality constraints and a set constraint where the constraining convex set is not necessarily open or closed. Under suitable generalized convexity assumptions we derive a weak, strong and strict converse duality theorem. By means of a suitable transformation of variables these results are then applied to a class of fractional programs involving a ratio of a convex and an affine function with a set constraint in addition to inequality and equality constraints. The results extend classical fractional programming duality without a set constraint involving a convex set that is not necessarily open or closed.

Duality in fractional programming problems with set constraints

CAMBINI, RICCARDO;CAROSI, LAURA;
2005-01-01

Abstract

Duality is studied for a minimization problem with finitely many inequality and equality constraints and a set constraint where the constraining convex set is not necessarily open or closed. Under suitable generalized convexity assumptions we derive a weak, strong and strict converse duality theorem. By means of a suitable transformation of variables these results are then applied to a class of fractional programs involving a ratio of a convex and an affine function with a set constraint in addition to inequality and equality constraints. The results extend classical fractional programming duality without a set constraint involving a convex set that is not necessarily open or closed.
2005
Cambini, Riccardo; Carosi, Laura; S., Schaible
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/175526
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