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 “An artificial-free simplex-type algorithm for general LP models” [Math. Comput. Model., 25 (1997), pp. 107–123] and “Initialization of the simplex algorithm: An artificial-free approach” [SIAM Rev., 39 (1997), pp. 736–744], Arsham presents a new Phase 1 algorithm for the simplex method of linear programming, which allegedly obviates the use of artificial variables. He claims in [SIAM Rev., ...

This note considers some aspects of the computational problem of by minimizing the sum of absolute deviations Yt = t 1 x· t l3· l= l l fitting the regression model (t = 1, 2, ... , n) r!: 1 x· t l3·1 l= l l The iterative method recently proposed by Schlossmacher (1973) is shown to have undesirable features under certain conditions. The linear programming approach using the simplex method as sug...

This note considers some aspects of the computational problem of k fitting the regression model Yt ~ ti~l Xit~i +~t (t ~ 1, 2, ... , n) by minimizing the sum of absolute deviations ~~lIYt ~=l Xit~il The iterative method recently proposed by Schlossmacher (1973) is shown to have undesirable features under certain conditions. The linear programming approach using the simplex method as suggested b...

Polytope complexes are the generalisation of polygon meshes in geoinformation systems (GIS) to arbitrary dimension, and a natural concept for accessing spatio-temporal information. Complexes of each dimension have a straightforward dimension-independent database representation called Relational Complex. Accordingly, complex overlay is the corresponding generalisation of map overlay in GIS to ar...

In this paper, a method based on Nelder and Mead’s simplex search method, is developed for solving multi-objective optimization problems. Unlike other multi-objective optimization algorithms based on classical methods, this method does not require any a priori knowledge about the problem. Moreover, it does not need any pre-defined weights or additional constraints as it works without scalarizin...

An interesting concept associated with linear programs is that of duality. For every LP problem there is a second LP problem with which it is intrinsically paired. This second LP problem can bound the feasible values of the first problem and even help find the optimal value to that problem. The initial LP problem is called the primal LP while the second is referred to as the dual LP. Consider t...