Abstract
We present a geometrical interpretation of the weighting method for constrained (finite dimensional) vector optimization. This approach is based on rigid movements which separate the image set from the negative of the ordering cone. We study conditions on the existence of such translations in terms of the boundedness of the scalar problems produced by the weighting method. Finally, using recession cones, we obtain the main result of our work: a sufficient condition under which weighting vectors yield solvable scalar problems.
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Dedicated to Clovis Gonzaga on the occasion of his 60th birthday.
B.F. Svaiter was partially supported by CNPq Grants 302748/2002-4, 476842/2003-4 and by PRONEX-Optimization (FAPERJ/CNPq).
L.M. Graña Drummond was partially supported by CNPq Grant 476842/2003-4 and by PRONEX-Optimization (FAPERJ/CNPq).
An erratum to this article can be found at http://dx.doi.org/10.1007/s10107-007-0108-6
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Drummond, L.M.G., Maculan, N. & Svaiter, B.F. On the choice of parameters for the weighting method in vector optimization. Math. Program. 111, 201–216 (2008). https://doi.org/10.1007/s10107-006-0071-7
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DOI: https://doi.org/10.1007/s10107-006-0071-7