A Study on Multiplicative Mathematical Programming Problems

Abstract

This thesis deals with the development of basic theoretical results as well as algorithms for solving multiplicative programming problems. During the 1990s, there has been a resurgence of interest in the multiplicative programming problem. This interest arises from two factors. First, linear multiplicative programming problems arise in a variety of practical applications. For example these include economic analysis ,VLSI chip design and bond portfolio construction. Second, encouraged by rapid advance in high-speed computing, researchers in recent years have been developing and testing new methods for solving global optimization problems in practice, including multiplicative programming problems. The general plan of this thesis, that contains five Chapters, is devoted to present a survey on linear multiplicative programming problems and to introduce a new algorithms to solve the problem The first chapter gives a survey of some definitions and fundamental results of linear programming, convex sets, convex and concave functions and duality theory in linear mathematical programming. Chapter 2 is devoted to introduce some basic concepts and some results of the theory of nonlinear programming. In chapter 3 we present a background on linear multiplicative programming problems Chapter 4 presents an algorithm for finding a global solution of linear multiplicative programming problem. The idea of this algorithm is based on using a successive partitioning approach, in each step of partitioning we will make a linear transformation. It is expected that considerable computational saving can be expected over the decision set­ based algorithms that have been proposed, in previous work, for the problem.