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On the choice of parameters for the weighting method in vector optimization |
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| Authors: | L M Grañax Drummond N Maculan B F Svaiter |
| Institution: | 1. Faculdade de Administra??o e Ciências Contábeis, FACC–UFRJ, Pasteur 250, Rio de Janeiro, RJ, CEP 22290-240, Brazil 2. Programa de Engenharia de Sistemas de Computa??o, COPPE–UFRJ, CP 68511, Rio de Janeiro, RJ, CEP 21945-970, Brazil 3. Instituto de Matemática Pura e Aplicada (IMPA), Estrada Dona Castorina 110, Rio de Janeiro, RJ, CEP 22460-320, Brazil |
| 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. An erratum to this article can be found at |
| Keywords: | Vector optimization Weak efficiency Scalarization Weighting method Recession cone |
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