An equivalent transformation of multi-objective optimization problems
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A new equivalent definition of proper efficiency is presented. With the aid of the new definition of properness, a transformation technique is proved to transform a multi-objective problem to a more convenient one. Some conditions are determined under which the original and the transformed problems have the same Pareto and properly efficient solutions. This transformation could be employed for the sake of convexification and simplification in order to improve the computational efficiency for solving the given problem. Moreover, some existing results about the weighted sum method in the multi-objective optimization literature are generalized using the special case of the proposed transformation scheme.
KeywordsMulti-objective optimization Vector optimization Proper efficiency Pareto optimality
P.M. Pardalos is partially supported by NSF, and by LATNA Laboratory, NRU HSE, RF government grant, ag. 11.G34.31.0057.
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