The goal of this research is to develop a potential reduction algorithm, based on recent results for analytic centers and their associated potential functions, that (1) allows column generation, (2) whose complexity does not depend on the full system of constraints and (3) that is implementable with practical efficiency. This type of a technique permits a great deal of flexibility for solving such optimization programs as semi-infinite programs, convex nonlinear programs and combinatorial optimization problems, in which the number of constraints is very large or some constraints are not explicitly known.
