The geometric programming problem

The aim of this thesis is to investigate the theory and methods of the geometric programming problem. The stress of the presentation is placed on the methods for solving the problem as well as the proofs of the theorems, which reveal the nature of the geometric programming problem and form the bases of the methods.

The first two chapters discuss the properties of the (posynomial) geometric programming problem and the methods for solving the problem.

Chapter I gives a discussion on the dual method, which solves the geometric programming problem via an indirect approach, and its theoretic basis.

Chapter II presents the primal method, which finds the solutions of the geometric programming problem directly but approximately, and its theoretic basis. The last two chapters discuss the properties of the generalized geometric programming problem, that is, signomial geometric programming problem, and the methods for solving the problem.

Chapter Ill presents the general features of the signomial geometric programming problem and the method for solving the problem by way of transforming the problem to complementary geometric programming.

Chapter IV gives a discussion about the properties of reversed geometric programming, which is a special case of signomial geometric programming, and the method for solving the problem. In fact, this method, which can be seen as a supplement for that presented in chapter Ill, shows another approach to solve the signomial geometric programming problem.