Transcendental Optimization in Geometric Programming via Power Series Approximations

Transcendental Geometric Programming (TGP) is an extension of classical Geometric Programming that involves transcendental functions such as exponential, logarithmic, and trigonometric functions. In this paper, we consider a class of TGP problems in which the variables appear as exponential functions in both the objective function and the constraints. As a first step, we expand the exponential function using power series expansions, thereby reducing the Transcendental Geometric Programming Problem (TGPP) to a Standard Geometric Programming Problem (SGPP). Multiple cases of SGPP are then generated by truncating the power series to the first, second and third terms. Each of these cases is solved separately by converting the resulting SGPPs into linear programming problems using the Karush-Kuhn-Tucker (KKT) conditions and Taylor series approximations. This methodology leads us to derive the optimal solutions for the problem. Finally, Python programming is used to solve the problem.