Preprint A343/2004
A Geometric Approach to the Weighting Method Scalarization in Vector Optimization
Benar Fux Svaiter | Grana Drummon, Luis Mauricio | Maculan, M.
Keywords: vector optimization | weak efficiency | scalarization | weighting method | recession cone
We consider the weighting method for constrained (finite dimensional) vector optimization. First we show that the closest points in the objective's image from certain hyperplanes are weakly efficient; this approach allows us to give a geometrical interpretation of the method. We also give some conditions on the the existence of weakly efficient optima, based on the connection between the recession cone of the convex hull of the objective's image and the negative of the ordering cone.