Geometric Programming is an established technique for solving certain classes of algebraic, nonlinear optimization problems. It has been applied to problems in a variety of areas, and has been especially useful in engineering design. In this project, an alternative approach to geometric programming will be analyzed which replaces the nonlinear primal-dual pair with a linear equivalent. Specifically, the project will (1) develop, code, test, and implement and algorithm based on the reformulation,(2) adapt sensitivity analysis procedures from linear optimization to geometric programming, (3) adapt linear programming decomposition principles to large geometric programming problems where the constraint sets can be partitioned based on the design variables that appear in them, (4) characterize multiple optima in geometric problems which possess the same, and (5) explore the approximation of certain classes of general nonlinear programs by geometric programming.
