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Super efficiency in vector optimization. (English) Zbl 0796.90045

After some comprehensive remarks on cones the authors introduce super efficiency as a new concept of proper efficiency in multicriteria optimization in half ordered real normed linear spaces X: If S is the ordering cone of X, C a nonempty subset of X, then xX is called a super efficient point of X with respect to S, if there is a real number M>0 such that cone (C-X)(B-S)MB, where B is the closed unit ball of X. They carefully compare super efficiency with proper efficiency in the senses of Borwein, Henig, Geoffrion, Hartly and with efficiency at all. For finite dimensions the new concept coincides with proper efficiency.

Furthermore, the authors prove an existence theorem for super efficient points, norm denseness results (in the efficient frontier) and characterizations.


MSC:
90C29Multi-objective programming; goal programming
90C48Programming in abstract spaces