Geometric Programming

• Published in: Engineering Optimization p. 1
• Main Author: Rao, Singiresu S
• Format: Book Chapter
• Language: English
• Published: United States John Wiley & Sons 2020; John Wiley & Sons, Incorporated; John Wiley & Sons, Inc
• Edition: 5th Edition
• Subjects: arithmetic‐geometric inequality; complementary geometric programming; constrained geometric programming problem; differential calculus; General Engineering & Project Administration; General References; mixed inequality constraints; posynomial; unconstrained geometric programming program; unconstrained minimization problem
• ISBN: 1119454719; 9781119454717
• DOI: 10.1002/9781119454816.ch8

Geometric programming is a relatively new method of solving a class of nonlinear programming problems compared to general NLP. If the natural formulation of the optimization problem does not lead to posynomial functions, geometric programming techniques can still be applied to solve the problem by replacing the actual functions by a set of empirically fitted posynomials over a wide range of the parameters. The solution of the unconstrained minimization problem can be obtained by various procedures. The chapter presents two approaches – one based on the differential calculus and the other based on the concept of geometric inequality – for the solution of the problem. Most engineering optimization problems are subject to constraints. If the objective function and all the constraints are expressible in the form of posynomials, geometric programming can be used most conveniently to solve the optimization problem. The chapter considers the solution of the constrained minimization problem.