A lot of research has been done to 1nd a faster (polynomial) algorithm that can solve linear programming (LP) problems. The main branch of this research has been devoted to interior point methods (IPM). The IPM outperforms the Simplex method in large LPs. However, there is still much research being done in order to improve pivoting algorithms. In this paper, we present a new approach to the pro...

This paper considers a biobjective transportation problem with various fuzzy objective functions coefficients. Fuzzy coefficients can be of different types such as triangular, trapezoidal, (semi) $L-R$, or flat (semi) $L-R$ fuzzy numbers. First, we convert the problem to a parametric interval biobjective transportation problem using $gamma$-cuts of fuzzy coefficients. Then, we consider a fix $g...

The simplex algorithm computes the simplex multipliers by solving a system (or two triangular systems) at each iteration. This note offers an efficient approach to updating the simplex multipliers in conjunction with the Bartels-Golub and Forrest-Tomlin updates for LU factors of the basis. It only solves one triangular system. The approach was implemented within and tested against MINOS 5.51 on...

Determining whether there is an integer point in an n-dimensional simplex is an NPcomplete problem. In this paper, a new arbitrary starting variable dimension algorithm is developed for computing an integer point of an n-dimensional simplex. The algorithm is derived from an introduction of an integer labeling rule and an application of a triangulation of the space and is composed of two phases,...

DYLP is a linear programming code implementing a dynamic simplex algorithm similar to that outlined by Padberg in [5]. The code attempts to maintain a reduced active constraint system by regularly purging loose constraints and variables with unfavourable reduced costs, and adding violated constraints and variables with favourable reduced costs. In abstract, the code alternates between primal an...

The paper addresses tlie design of tlie polyphase IIR filters based on the “’-order single-coefficient allpass sub-filters in the constraint coefficient space using the Constraint Dowdiill Simplex Algorithm. Incorporating the bit-flipping algorithm into its core engine allowed the optitilisation routine to converge to better target designs without affecting tlie Iiigli speed of tlie original al...

We define a weak compatibility condition for the Newest Vertex Bisection algorithm on simplex grids of any dimension and show that using this condition the iterative algorithm terminates successfully. Additionally we provide an O(n) algorithm that renumbers any simplex grid to fulfil this condition. Furthermore we conduct experiments to estimate the distance to the standard compatibility and al...

A geometrical analysis is made of the dual simplex algorithm applied to a linear programming formulation of the one-center location problem in IR (2) using block distance. A geometric rule is given, and shown to be equivalent to the minimum ratio rule of the simplex algorithm, for updating the dual basis. The geometric analysis is applied to the Euclidean distance one-center problem and yields ...

A discrete statistical model is a subset of probability simplex. Its maximum likelihood estimator (MLE) retraction from that simplex onto the model. We characterize all models for which this rational function. This contribution via real algebraic geometry rests on results Horn uniformization due to Huh and Kapranov. present an algorithm constructing with MLE, we demonstrate it range instances. ...