Goal-programming mit L_p-metriken

Abstract

The usual goal programming approach is generalized to the case, where the set of “alternatives” is a closed, convex set of functions on a compact set K and the L_p -metric is used. The main results concern the continuity and monotonicity of and of the minimizing functions . They are new even in the case . For finite K the convergence of f_p , as p → ∞, is proved. If K = {1, 2}, it is seen that and are monotone, whereas an example with K = {1, 2, 3} shows that these properties cannot be generalized.