The paper explores the use of the Shannon (informational) entropy measure and Jaynes's maximum entropy formalism in the solution of constrained non-linear programming problems. Through a surrogate constraint approach an entropy based update formula for the surrogate multipliers is derived. A numerical example of the method is presented. Some information-theoretic interpretations of mathematical programming are explored. Finally, through the use or surrogate duals the method is extended into an entropy augmented Lagrangean formulation.