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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.