  We treat uncertain linear programming problems by utilizing the notion of
weighted analytic centers and notions from the area of multi-criteria decision
making. After introducing our approach, we develop interactive cutting-plane
algorithms for robust optimization, based on concave and quasi-concave utility
functions. In addition to practical advantages, due to the flexibility of our
approach, we are able to prove that under a theoretical framework due to
Bertsimas and Sim [14], which establishes the existence of certain convex
formulation of robust optimization problems, the robust optimal solutions
generated by our algorithms are at least as desirable to the decision maker as
any solution generated by many other robust optimization algorithms in the
theoretical framework. We present some probabilistic bounds for feasibility of
robust solutions and evaluate our approach by means of computational
experiments.
