An Analysis of Some Dual Problems in Multiobjective Optimization (i)
نویسندگان
چکیده
In this work we study the duality for a general multiobjective optimization problem. Considering, first, a scalar problem, different duals using the conjugacy approach are presented. Starting from these scalar duals, we introduce six different multiobjective dual problems to the primal one, one depending on certain vector parameters. The existence of weak and, under certain conditions, of strong duality between the primal and the dual problems is shown. Afterwards, some inclusion results for the image sets of the multiobjective dual problems (D1), (Dα) and (DFL) are derived. Moreover, we verify that the efficiency sets within the image sets of these problems coincide, but the image sets themselves do not.
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An Analysis of Some Dual Problems in Multiobjective Optimization (ii)
In the first part of this study we have introduced six different multiobjective dual problems to a general multiobjective optimization problem, for which we presented weak as well as strong duality assertions. Afterwards, we derived some inclusion results for the image sets of three of these problems. The aim of this second part is to complete our investigations by studying the relations betwee...
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