In this paper we address a general Goal Programming problem with linear objectives, convex constraints, and an arbitrary componentwise nondecreasing norm to aggregate deviations with respect to targets. In particular, classical Linear Goal Programming problems, as well as several models in Location and Regression Analysis are modeled within this framework.

In spite of its generality, this problem can be analyzed from a geometrical and computational viewpoint, and a unified resolution methodology can be given. Indeed, a dual is derived as a direct consequence of standard minimax theorems, enabling us to describe the set of optimal solutions geometrically. Moreover, Interior-Point methods are described which yield an $\varepsilon$-optimal solution in polynomial time.

Keywords: Goal Programming, Closest points, Interior point methods, Location, Regression.