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 by allowing for a set constraint involving a convex set that is not necessarily open or closed.
This research has been partially supported by M.I.U.R. and C.N.R.
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Cambini, R., Carosi, L., Schaible, S. (2005). Duality in Fractional Programming Problems with Set Constraints. In: Eberhard, A., Hadjisavvas, N., Luc, D.T. (eds) Generalized Convexity, Generalized Monotonicity and Applications. Nonconvex Optimization and Its Applications, vol 77. Springer, Boston, MA. https://doi.org/10.1007/0-387-23639-2_8
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DOI: https://doi.org/10.1007/0-387-23639-2_8
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