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.