We present a Simplex-type algorithm, that is, an algorithm that moves from one extreme point of the infinite-dimensional feasible region to another not necessarily adjacent extreme point, for solving a class of linear programs with countably infinite variables and constraints. Each iteration of this method can be implemented in finite time, while the solution values converge to the optimal valu...

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...

We present Barrier-based Simplex (Bb-Simplex), a new, provably correct design for runtime assurance of continuous dynamical systems. Bb-Simplex is centered around the Control Architecture, which consists high-performance advanced controller not guaranteed to maintain safety plant, verified-safe baseline controller, and decision module that switches control plant between two controllers ensure w...

Lednicki and Wieczorkowski (2003) presented a method of stratification in subpopulations, based on the paper of Rivest (2002), which leads to obtain a fixed precision of a considered estimator for the particular subpopulations. They solved such a problem using a numerical simplex method of Nelder and Mead (1965). Because it is not the best solution of the question, (in a sense of an optimality ...

The transshipment problem is one of the central problems in network optimization. There exist several polynomial and strongly polynomial algorithms for solving this problem (see the surveys [7, 1]). Nevertheless, the method of choice in practice still seems to be the network simplex method. In this paper we shall consider the dual network simplex method. We show that some excess scaling algorit...

The simplex method is perhaps the most widely used method for solving linear programming (LP) problems. The computation time of simplex type algorithms depends on the basis inverse that occurs in each iteration. Parallelizing simplex type algorithms is one of the most challenging problems. The aim of this paper is to present a parallel implementation of the primal exterior point simplex algorit...

The Nelder-Mead simplex method is an optimization routine that works well with irregular objective functions. For a function of n parameters, it compares the objective function at the n + 1 vertices of a simplex and updates the worst vertex through simplex search steps. However, a standard serial implementation can be prohibitively expensive for optimizations over a large number of parameters. ...

Recent work in mathematical neuroscience has calculated the directed graph homology of simplicial complex given by brains sparse adjacency graph, so called connectome. These biological connectomes show an abundance both high-dimensional simplices and Betti-numbers all viable dimensions - contrast to Erd\H{o}s-R\'enyi-graphs comparable size density. An analysis synthetically trained reveals simi...

Linear programming has many important practical applications, and has also given rise to a wide body of theory. See Section 49.9 for recommended sources. Here we consider the linear programming problem in the form of maximizing a linear function of d variables subject to n linear inequalities. We focus on the relationship of the problem to computational geometry, i.e., we consider the problem i...

In this paper, we show that the parametric simplex method is an efficient algorithm for solving various statistical learning problems that can be written as linear programs parametrized by a so-called regularization parameter. The parametric simplex method offers significant advantages over other methods: (1) it finds the complete solution path for all values of the regularization parameter by ...