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Quasimin and quasisaddlepoint for vector optimization
Authors:B D Craven
Institution:Mathematics Department , University of Melbourne , Parkville, Vic, 3052, Australia
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.
Keywords:Decomposition spaces  Discrete convolutions  Function spaces inclusions  Sampling theory  Wavelets  Mathematics Subject Classifications 2000: 46S30  94A20  65T50  65T60
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