Linear programming (LP) is an important tool for many inter-disciplinary optimization problems. The Simplex method is the most widely used algorithm to solve LP problems and has immense impact on several developments in various fields. With development of public domain and commercial software solvers, it has been automated and made available for use. A serious bottleneck in implementation of Si...

The pupose of this paper is modeling of Partial Digest Problem (PDP) as a mathematical programming problem. In this paper we present a new viewpoint of PDP. We formulate the PDP as a continuous optimization problem and develope a method to solve this problem. Finally we constract a linear programming model for the problem with an additional constraint. This later model can be solved by the simp...

We first introduce matrix concepts in linear programming by developing a variation of the simplex method called the revised simplex method. This algorithm, which has become the basis of all commercial computer codes for linear programming, simply recognizes that much of the information calculated by the simplex method at each iteration, as described in Chapter 2, is not needed. Thus, efficienci...

The simplex algorithm requires artificial variables for solving linear programs, which lack primal feasibility at the origin point. We present a new general-purpose solution algorithm, called Push-and-Pull, which obviates the use of artificial variables. The algorithm consists of preliminaries for setting up the initialization followed by two main phases. The Push Phase develops a basic variabl...

Linear Programming is a significant and well-studied optimization methodology. Simplex type algorithms have been widely used in Decision Support Systems. The computation of the basis inverse is a crucial step in simplex type algorithms. In this paper, we review and compare three basis update methods. We incorporate these methods on the exterior and the revised simplex algorithm in order to high...

in this paper, the energy efficient resource allocation in noma-based heterogeneous cellular network(hcn) systems is investigated. since energy consumption and its limitations is one of the important challenges in fifth generation of cellular networks (5g), we propose a resource allocation problem which allocates power and subcarriers to multiple users to achieve the best system energy efficien...