Quasimin and quasisaddlepoint for vector optimization |
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Authors: | B D Craven |
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Institution: | Mathematics Department , University of Melbourne , Parkville, Vic, 3052, Australia |
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Abstract: | For a constrained multicriteria optimization problem with differentiable functions, but not assuming any convexity, vector analogs of quasimin, Kuhn-Tucker point, and (suitably defined) vector quasisaddlepoint are shown to be equivalent. A constraint qualification is assumed. Similarly, a proper (by Geoffrion's definition) weak minimum is equivalent to a Kuhn–Tucker point with a strictly positive multiplier for the objective, and also to a vector quasisaddlepoint with an attached stability property. Under generalized invex hypotheses, these properties reduce to proper minimum and stable saddlepoint. Various known results are thus unified. |
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Keywords: | Decomposition spaces Discrete convolutions Function spaces inclusions Sampling theory Wavelets Mathematics Subject Classifications 2000: 46S30 94A20 65T50 65T60 |
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