This paper introduces the design and implementation of two parallel dual simplex solvers for general large scale sparse linear programming problems. One approach, called PAMI, extends a relatively unknown pivoting strategy called suboptimization and exploits parallelism across multiple iterations. The other, called SIP, exploits purely single iteration parallelism by overlapping computational c...

• By convention, the vector formed by taking together all the basic variables is denoted xB. Similarly, cB, `B and uB are formed by taking together the same indices of c, ` and u, respectively. The same notation is also used for the indices in L and U , giving cL, cU , `L, `U , uL, and uU . We already defined B as taking together the basic columns of A. The remaining (nonbasic) columns form the...

Abstract. The paper focuses its attention on solving Multi-objective intuitionistic fuzzy linear programming problem and Multi-objective intuitionistic fuzzy linear fractional programming problem by using weighting factor in which the constraints and the cost coefficients are intuitionistic fuzzy numbers. Weighting factor is used to convert problems that are multi-objective into single objectiv...

A new method namely, denominator objective restriction method based on simplex method is proposed for solving linear fractional programming problems. Further, another method namely, decomposition-restriction method based on decomposition principle and the denominator objective restriction method is proposed for obtaining an optimal fuzzy solution to the fully fuzzy linear fractional programming...

this paper deals with ridge estimation of fuzzy nonparametric regression models using triangular fuzzy numbers. this estimation method is obtained by implementing ridge regression learning algorithm in the la- grangian dual space. the distance measure for fuzzy numbers that suggested by diamond is used and the local linear smoothing technique with the cross- validation procedure for selecting t...

Real-life linear programming (LP) problems include all types of variables and constraints. Current versions of the primal simplex method are well prepared to handle such problems efficiently. At the same time, the usefulness of the dual simplex method was thought to be limited to the standard problem though it could be the ideal algorithm in many other cases. For instance, most solution methods...

In this short paper, we give an upper bound for the number of different basic feasible solutions generated by the dual simplex method with the most negative pivoting rule for LP. The bound is comparable with the bound given by Kitahara and Mizuno (2010) for the primal simplex method. We apply the result to the maximum flow problem and get a strong polynomial bound.

In case of a special problem class, the simplex method can be implemented as a cutting-plane method that approximates a polyhedral convex objective function. In this paper we consider a regularized version of this cutting-plane method, and interpret the resulting procedure as a regularized simplex method. (Regularization is performed in the dual space and only affects the process through the pr...