This paper shows that the optimal simplex, in the sense of minimizing the linear interpolation error of the quadratic function u(x) = x2 measured in Lp-norm, is the equilateral simplex. It also contains several explicit formulae on the best interpolation error when the volume of the simplex is one.

The revised simplex method is often the method of choice when solving large scale sparse linear programming problems, particularly when a family of closely-related problems is to be solved. Each iteration of the revised simplex method requires the solution of two linear systems and a matrix vector product. For a significant number of practical problems the result of one or more of these operati...

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...

L1 norm estimator has been widely used as a robust parameter estimation method for outlier detection. Different algorithms have been applied for L1 norm minimization among which the linear programming problem based on the simplex method is well known. In the present contribution, in order to solve an L1 norm minimization problem in a linear model, an interior point algorithm is developed which ...

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 ...

This study is devoted to address the notion of duality in Fully Intuitionistic Fuzzy Linear Programming Problems (FIFLP). The problem is addressed by using a revised simplex method with the Gaussian elimination process in fully intuitionistic fuzzy environment. Intuitionistic Fuzzy Trapezoidal Numbers (IFTrpN), along with the basic arithmetic techniques defined on them help in solving the (FIFL...

This paper presents a fast algorithm to optimize both the widths and lengths of power/ground networks under reliability and power dip/ground bounce constraints. The spacesizing which allows the length to change gives more flexibility in solving practical problems. There are two major contributions of this paper. First, we prove that for general topology, a relaxed version of this problem is als...

This paper introduces three novel techniques for updating the invertible representation of the basis matrix when solving practical sparse linear programming (LP) problems using a high performance implementation of the dual revised simplex method, being of particular value when suboptimization is used. Two are variants of the product form update and the other permits multiple Forrest-Tomlin upda...

In this paper, we generalize the concept of sensitivity analysis in fuzzy number linear programming (FLNP) problems by applying fuzzy simplex algorithms and using the general linear ranking functions on fuzzy numbers. The purpose of sensitivity analysis is to determine changes in the optimal solution of FNLP problem resulting from changes in the data. If the change affects the optimality of the...