Applications of Generalized Inverses to Interval Linear Programs in Hilbert Spaces

Let H1 and H2 be real Hilbert spaces. Suppose H2 is partially 2 ordered, a, b ε H2, c ε H1 and A :H1→H2is a continuous linear 21 12 map. We consider the following interval linear program: Maximize <c, x> subject to a ≤Ax ≤ b. Conditions under which explicit solutions to the above problem can be found are studied. The solutions are represented in terms of generalized inverses of A. Several examples are given to illustrate the main results. © 1995, Taylor & Francis Group, LLC. All rights reserved.