In this paper, He’s homotopy perturbation method (HPM) is applied for solving linear programming (LP) problems. This paper shows that some recent findings about this topic cannot be applied for all cases. Furthermore, we provide the correct application of HPM for LP problems. The proposed method has a simple and graceful structure. Finally, a numerical example is displayed to illustrate the pro...

A fast Newton method is proposed for solving linear programs with a very large (≈ 10) number of constraints and a moderate (≈ 10) number of variables. Such linear programs occur in data mining and machine learning. The proposed method is based on the apparently overlooked fact that the dual of an asymptotic exterior penalty formulation of a linear program provides an exact least 2-norm solution...

Conflict-Driven Clause-Learning (CDCL) SAT solvers can automatically solve very large real-world problems. To go beyond, and in particular in order to solve and optimize problems involving linear arithmetic constraints, here we introduce IntSat, a generalization of CDCL to Integer Linear Programming (ILP). Our simple 1400-line C++ prototype IntSat implementation already shows some competitivene...

G eorge Dantzig, in describing the " Origins of the Simplex Method, " 1 noted that it was the availability of early digital computers that supported and invited the development of LP models to solve real-world problems. He agreed that invention is sometimes the mother of necessity. Moreover, he commented that he initially rejected the simplex method because it seemed intuitively more attractive...

We discuss the method recently proposed by S. Chubanov for the linear feasibility problem. We present new, concise proofs and geometric interpretations of some of his results. From our ideas we derive the first strongly polynomial time algorithm based on relaxation method techniques for special classes of linear feasibility problems. Under certain conditions, these results provide new proofs of...

To my beloved wife, Yuijn iii ACKNOWLEDGEMENTS First, I want to thank my wife Yujin for her enduring patience and loving support during my study. She has been always there for me from the very beginning to this very end. She has been at the core of my motivation even when I was doubting if could finish this program. I also have to mention my beloved children, Lynn and Olivia, who have been an e...

In this paper, ellipsoid method for linear programming is derived using only minimal knowledge of algebra and matrices. Unfortunately, most authors first describe the algorithm, then later prove its correctness, which requires a good knowledge of linear algebra.