Using weighting vectors to solve multiple attribute problems: A framework

In this paper a study is made of the use of weighting vectors to generate solutions to problems where the gradient vectors are known to be in a given set. A measure of closeness of weighting vectors and of objective function vectors generated, is developed, and, in the latter case, using various semi-norms, surrogate optimization problems are developed to assess this closeness at any stage of, for example, an interactive method. The semi-norms are then related to the underlying value function gradients to give conditions for terminating the procedure.