Closing the duality gap in linear vector optimization
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Using a set-valued dual cost function we give a new approach to duality theory for linear vector optimization problems. We develop the theory very close to the scalar case. Especially, in contrast to known results, we avoid the appearance of a duality gap in case of b = 0. Examples are given.
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Hamel, AH (TAYLOR & FRANCIS LTD, 2011)A duality theorem of the Fenchel-Rockafellar type for set-valued optimization problems is presented along with a result for the conjugate of the sum of two set-valued functions and a chain rule. The underlying solution ...
Hamel, AH; Loehne, A (Springer Verlag (Germany), 2014)Based on the complete-lattice approach, a new Lagrangian type duality theory for set-valued optimization problems is presented. In contrast to previous approaches, set-valued versions for the known scalar formulas involving ...
Hamel, AH (SPRINGER, 2009)It is proven that a proper closed convex function with values in the power set of a preordered, separated locally convex space is the pointwise supremum of its set-valued affine minorants. A new concept of Legendre-Fenchel ...