Transcendental Optimization in Geometric Programming via Power Series Approximations

his research introduces a systematic method for solving Transcendental Geometric Programming (TGP) problems where variables appear as exponential terms in both objective functions and constraints. By expanding transcendental functions into power series and truncating at successive terms, the TGP is reduced to Standard Geometric Programming Problems (SGPP) solvable through Karush–Kuhn–Tucker (KKT) conditions and Taylor series linearization. Computational implementation in Python (Google Colab) verifies convergence, stability, and feasibility across multiple truncation levels. Results show that third-order approximations yield efficient, accurate, and computationally stable solutions, making this methodology suitable for real-world optimization scenarios involving transcendental behavior.