The classical simplex method is extended into the Semiglobal Simplex (SGS) algorithm. Although SGS does not guarantee finding the global minimum, it affords a much more thorough exploration of the local minima than any traditional minimization method. The basic idea of SGS is to perform a local minimization in each step of the simplex algorithm, and thus, similarly to the Convex Global Underest...

Kitahara and Mizuno get new bounds for the number of distinct solutions generated by the simplex method for linear programming (LP). In this paper, we combine results of Kitahara and Mizuno and Tardos’s strongly polynomial algorithm, and propose an algorithm for solving a standard form LP problem. The algorithm solves polynomial number of artificial LP problems by the simplex method with Dantzi...

Two existing methods for solving a class of fuzzy linear programming (FLP) problems involving symmetric trapezoidal fuzzy numbers without converting them to crisp linear programming problems are the fuzzy primal simplex method proposed by Ganesan and Veeramani [1] and the fuzzy dual simplex method proposed by Ebrahimnejad and Nasseri [2]. The former method is not applicable when a primal basic ...

Cutting plane methods require the solution of a sequence of linear programs where the solution to one provides a warm start to the next A cutting plane algorithm for solving the linear ordering problem is described This algorithm uses the primal dual interior point method to solve the linear programming relaxations A point which is a good warm start for a simplex based cutting plane algorithm i...

We propose a variation of simplex-downhill algorithm specifically customized for optimizing parameters in statistical machine translation (SMT) decoder for better end-user automatic evaluation metric scores for translations, such as versions of BLEU, TER and mixtures of them. Traditional simplexdownhill has the advantage of derivative-free computations of objective functions, yet still gives sa...

There has been a great deal of success in the last twenty years with the use of cutting plane algorithms to solve specialized integer programming problems. Generally, these algorithms work by solving a sequence of linear programming relaxations of the integer programming problem, and they use the simplex algorithm to solve the relaxations. In this paper, we describe experiments using a predicto...

Zuni´c. On the maximal number of edges of convex digital polygons included into a square grid. A simplex variant solving an m ×d linear program in O (min(m 2 , d 2)) expected number of pivot steps. A simplex algorithm whose average number of steps is bounded between two quadratic functions of the smaller dimension. 12 P. K. Agarwal. A deterministic algorithm for partitioning arrangements of lin...

In this paper we investigate the usage of the Lagrangian approach as a mechanism of speeding up the optimal basis identification in simplex methods. More precisely, we have combined the volume algorithm (a variation of the subgradient algorithm) with a simplex implementation like Cplex on a strong linear programming formulation of the asymmetric traveling salesman problem known by extended disa...

Many ranking methods have been proposed so far. However, there is yet no method that can always give a satisfactory solution to every situation; some are counterintuitive, not discriminating; some use only the local information of fuzzy values; some produce different ranking for the same situation. For overcoming the above problems, we propose a new method for ranking fuzzy quantities based on ...

As a natural extension of the dual simplex algorithm, the dual face algorithm performed remarkably in computational experiments with a set of Netlib standard problems. In this paper, we generalize it to bounded-variable LP problems via local duality.